{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T13:58:55Z","timestamp":1772805535137,"version":"3.50.1"},"reference-count":77,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T00:00:00Z","timestamp":1655251200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T00:00:00Z","timestamp":1655251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"WCU ITB 2019"},{"name":"PPD Kemenristek 2020"},{"name":"Faculty Start-Up Grant","award":["No. 8474000351-FSU- 2021-011"],"award-info":[{"award-number":["No. 8474000351-FSU- 2021-011"]}]},{"name":"Riset ITB 2021"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s00332-022-09810-z","type":"journal-article","created":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T11:02:49Z","timestamp":1655290969000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Snakes on Lieb lattice"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1963","authenticated-orcid":false,"given":"R.","family":"Kusdiantara","sequence":"first","affiliation":[]},{"given":"F. T.","family":"Akbar","sequence":"additional","affiliation":[]},{"given":"N.","family":"Nuraini","sequence":"additional","affiliation":[]},{"given":"B. E.","family":"Gunara","sequence":"additional","affiliation":[]},{"given":"H.","family":"Susanto","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,15]]},"reference":[{"issue":"3","key":"9810_CR1","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1137\/100782747","volume":"9","author":"D Avitabile","year":"2010","unstructured":"Avitabile, D., Lloyd, D.J.B., Burke, J., Knobloch, E., Sandstede, B.: To snake or not to snake in the planar Swift\u2013Hohenberg equation. SIAM J. Appl. Dyn. Syst. 9(3), 704\u2013733 (2010)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"issue":"25","key":"9810_CR2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.253902","volume":"101","author":"S Barbay","year":"2008","unstructured":"Barbay, S., Hachair, X., Elsass, T., Sagnes, I., Kuszelewicz, R.: Homoclinic snaking in a semiconductor-based optical system. Phys. Rev. Lett. 101(25), 253902 (2008)","journal-title":"Phys. Rev. Lett."},{"issue":"9","key":"9810_CR3","doi-asserted-by":"publisher","DOI":"10.1063\/1.3626405","volume":"23","author":"C Beaume","year":"2011","unstructured":"Beaume, C., Bergeon, A., Knobloch, E.: Homoclinic snaking of localized states in doubly diffusive convection. Phys. Fluids 23(9), 094102 (2011)","journal-title":"Phys. Fluids"},{"issue":"2","key":"9810_CR4","doi-asserted-by":"publisher","DOI":"10.1063\/1.4792711","volume":"25","author":"C Beaume","year":"2013","unstructured":"Beaume, C., Bergeon, A., Knobloch, E.: Convectons and secondary snaking in three-dimensional natural doubly diffusive convection. Phys. Fluids 25(2), 024105 (2013)","journal-title":"Phys. Fluids"},{"issue":"10","key":"9810_CR5","doi-asserted-by":"publisher","first-page":"5461(R)","DOI":"10.1103\/PhysRevA.38.5461","volume":"38","author":"D Bensimon","year":"1988","unstructured":"Bensimon, D., Shraiman, B.I., Croquette, V.: Nonadiabatic effects in convection. Phys. Rev. A 38(10), 5461(R) (1988)","journal-title":"Phys. Rev. A"},{"key":"9810_CR6","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/11\/9\/093037","volume":"11","author":"U Bortolozzo","year":"2009","unstructured":"Bortolozzo, U., Clerc, M.G., Residori, S.: Solitary localized structures in a liquid crystal light-valve experiment. New J. Phys. 11, 093037 (2009)","journal-title":"New J. Phys."},{"key":"9810_CR7","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/926810","volume":"2009","author":"U Bortolozzo","year":"2009","unstructured":"Bortolozzo, U., Clerc, M.G., Haudin, F., Rojas, R.G., Residori, S.: Localized states in bi-pattern systems. Adv. Nonlinear Opt. 2009, 926810 (2009)","journal-title":"Adv. Nonlinear Opt."},{"issue":"1\u20136","key":"9810_CR8","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1016\/S0030-4018(03)01341-5","volume":"219","author":"G Boudebs","year":"2003","unstructured":"Boudebs, G., Cherukulappurath, S., Leblond, H., Troles, J., Smektala, F., Sanchez, F.: Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses. Opt. Commun. 219(1\u20136), 427\u2013433 (2003)","journal-title":"Opt. Commun."},{"issue":"7","key":"9810_CR9","doi-asserted-by":"publisher","first-page":"3500","DOI":"10.1088\/1361-6544\/ab7d1e","volume":"33","author":"JJ Bramburger","year":"2020","unstructured":"Bramburger, J.J., Sandstede, B.: Localized patterns in planar bistable weakly coupled lattice systems. Nonlinearity 33(7), 3500 (2020)","journal-title":"Nonlinearity"},{"key":"9810_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-10331-9","volume-title":"The Frenkel\u2013Kontorova Model: Concepts, Methods, and Applications","author":"OM Braun","year":"2004","unstructured":"Braun, O.M., Kivshar, Y., Kivshar, Y.S.: The Frenkel\u2013Kontorova Model: Concepts, Methods, and Applications. Springer, Berlin (2004)"},{"issue":"1","key":"9810_CR11","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1137\/110843976","volume":"11","author":"J Burke","year":"2012","unstructured":"Burke, J., Dawes, J.H.P.: Localised states in an extended Swift\u2013Hohenberg equation. SIAM J. Appl. Dyn. Syst. 11(1), 261\u2013284 (2012)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"9810_CR12","doi-asserted-by":"publisher","DOI":"10.1063\/1.2746816","volume":"17","author":"J Burke","year":"2007","unstructured":"Burke, J., Knobloch, E.: Homoclinic snaking: structure and stability. Chaos 17, 037102 (2007)","journal-title":"Chaos"},{"issue":"6","key":"9810_CR13","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1016\/j.physleta.2006.08.072","volume":"360","author":"J Burke","year":"2007","unstructured":"Burke, J., Knobloch, E.: Snakes and ladders: localized states in the Swift\u2013Hohenberg equation. Phys. Lett. A 360(6), 681\u2013688 (2007)","journal-title":"Phys. Lett. A"},{"issue":"1","key":"9810_CR14","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.physd.2006.01.022","volume":"216","author":"R Carretero-Gonz\u00e1lez","year":"2006","unstructured":"Carretero-Gonz\u00e1lez, R., Talley, J.D., Chong, C., Malomed, B.A.: Multistable solitons in the cubic\u2013quintic discrete nonlinear Schr\u00f6dinger equation. Physica D 216(1), 77\u201389 (2006)","journal-title":"Physica D"},{"issue":"11","key":"9810_CR15","doi-asserted-by":"publisher","first-page":"113046","DOI":"10.1088\/1367-2630\/ab56c1","volume":"21","author":"Y Chen","year":"2019","unstructured":"Chen, Y., Chen, H.: Photonic zero-energy modes in a metal-based Lieb lattice. New J. Phys. 21(11), 113046 (2019)","journal-title":"New J. Phys."},{"issue":"1","key":"9810_CR16","first-page":"1019","volume":"4","author":"C Chong","year":"2011","unstructured":"Chong, C., Pelinovsky, D.E.: Variational approximations of bifurcations of asymmetric solitons in cubic\u2013quintic nonlinear Schr\u00f6dinger lattices. Discrete Cont. Dyn. Syst. S 4(1), 1019\u20131032 (2011)","journal-title":"Discrete Cont. Dyn. Syst. S"},{"issue":"2","key":"9810_CR17","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.physd.2008.10.002","volume":"238","author":"C Chong","year":"2009","unstructured":"Chong, C., Carretero-Gonz\u00e1lez, R., Malomed, B.A., Kevrekidis, P.G.: Multistable solitons in higher-dimensional cubic\u2013quintic nonlinear Schr\u00f6dinger lattices. Physica D 238(2), 126\u2013136 (2009)","journal-title":"Physica D"},{"key":"9810_CR18","doi-asserted-by":"publisher","first-page":"109617","DOI":"10.1016\/j.chaos.2020.109617","volume":"133","author":"J Cisternas","year":"2020","unstructured":"Cisternas, J., Escaff, D., Clerc, M.G., Lefever, R., Tlidi, M.: Gapped vegetation patterns: crown\/root allometry and snaking bifurcation. Chaos Solitons Fractals 133, 109617 (2020)","journal-title":"Chaos Solitons Fractals"},{"issue":"15","key":"9810_CR19","doi-asserted-by":"publisher","first-page":"2906","DOI":"10.1364\/OL.42.002906","volume":"42","author":"MG Clerc","year":"2017","unstructured":"Clerc, M.G., Ferr\u00e9, M.A., Coulibaly, S., Rojas, R.G., Tlidi, M.: Chimera-like states in an array of coupled-waveguide resonators. Opt. Lett. 42(15), 2906\u20132909 (2017)","journal-title":"Opt. Lett."},{"key":"9810_CR20","doi-asserted-by":"publisher","DOI":"10.1063\/1.5133836","volume":"30","author":"MG Clerc","year":"2020","unstructured":"Clerc, M.G., Coulibaly, S., Ferr\u00e9, M.A., Tlidi, M.: Two-dimensional optical chimera states in an array of coupled waveguide resonators. Chaos 30, 043107 (2020)","journal-title":"Chaos"},{"issue":"14","key":"9810_CR21","doi-asserted-by":"publisher","first-page":"3069","DOI":"10.1103\/PhysRevLett.84.3069","volume":"84","author":"P Coullet","year":"2000","unstructured":"Coullet, P., Riera, C., Tresser, C.: Stable static localized structures in one dimension. Phys. Rev. Lett. 84(14), 3069 (2000)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"9810_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-019-13993-7","volume":"11","author":"B Cui","year":"2020","unstructured":"Cui, B., Zheng, X., Wang, J., Liu, D., Xie, S., Huang, B.: Realization of Lieb lattice in covalent-organic frameworks with tunable topology and magnetism. Nat. Commun. 11(1), 1\u20138 (2020)","journal-title":"Nat. Commun."},{"issue":"7","key":"9810_CR23","doi-asserted-by":"publisher","first-page":"2667","DOI":"10.1088\/1361-6544\/ab0b1d","volume":"32","author":"H De Witt","year":"2019","unstructured":"De Witt, H.: Beyond all order asymptotics for homoclinic snaking in a Schnakenberg system. Nonlinearity 32(7), 2667\u20132693 (2019)","journal-title":"Nonlinearity"},{"issue":"1","key":"9810_CR24","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1137\/140966897","volume":"14","author":"AD Dean","year":"2015","unstructured":"Dean, A.D., Matthews, P.C., Cox, S.M., King, J.R.: Orientation-dependent pinning and homoclinic snaking on a planar lattice. SIAM J. Appl. Dyn. Syst. 14(1), 481\u2013521 (2015)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"issue":"2","key":"9810_CR25","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1088\/0951-7715\/10\/2\/002","volume":"10","author":"B Dionne","year":"1997","unstructured":"Dionne, B., Silber, M., Skeldon, A.C.: Stability results for steady, spatially periodic planforms. Nonlinearity 10(2), 321 (1997)","journal-title":"Nonlinearity"},{"issue":"7","key":"9810_CR26","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1038\/nphys4080","volume":"13","author":"R Drost","year":"2017","unstructured":"Drost, R., Ojanen, T., Harju, A., Liljeroth, P.: Topological states in engineered atomic lattices. Nat. Phys. 13(7), 668\u2013671 (2017)","journal-title":"Nat. Phys."},{"issue":"7","key":"9810_CR27","doi-asserted-by":"publisher","first-page":"1010","DOI":"10.1364\/OL.38.001010","volume":"38","author":"OA Egorov","year":"2013","unstructured":"Egorov, O.A., Lederer, F.: Spontaneously walking discrete cavity solitons. Opt. Lett. 38(7), 1010 (2013)","journal-title":"Opt. Lett."},{"issue":"4","key":"9810_CR28","doi-asserted-by":"publisher","first-page":"2537","DOI":"10.1021\/acs.nanolett.9b05316","volume":"20","author":"H Feng","year":"2020","unstructured":"Feng, H., Liu, C., Zhou, S., Gao, N., Gao, Q., Zhuang, J., Xu, X., Hu, Z., Wang, J., Chen, L., Zhao, J., Dou, S.X., Du, Y.: Experimental realization of two-dimensional buckled Lieb lattice. Nano Lett. 20(4), 2537\u20132543 (2020)","journal-title":"Nano Lett."},{"issue":"3","key":"9810_CR29","doi-asserted-by":"publisher","DOI":"10.1063\/1.2768157","volume":"17","author":"WJ Firth","year":"2007","unstructured":"Firth, W.J., Columbo, L., Maggipinto, T.: On homoclinic snaking in optical systems. Chaos 17(3), 037115 (2007)","journal-title":"Chaos"},{"issue":"26","key":"9810_CR30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.264101","volume":"107","author":"F Haudin","year":"2011","unstructured":"Haudin, F., Rojas, R.G., Bortolozzo, U., Residori, S., Clerc, M.G.: Homoclinic snaking of localized patterns in a spatially forced system. Phys. Rev. Lett. 107(26), 264101 (2011)","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"9810_CR31","doi-asserted-by":"publisher","first-page":"2046","DOI":"10.1103\/PhysRevE.51.2046","volume":"51","author":"MF Hilali","year":"1995","unstructured":"Hilali, M.F., M\u00e9tens, S., Borckmans, P., Dewel, G.: Pattern selection in the generalized Swift\u2013Hohenberg model. Phys. Rev. E 51(3), 2046 (1995)","journal-title":"Phys. Rev. E"},{"issue":"1","key":"9810_CR32","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1023\/A:1008398006403","volume":"21","author":"GW Hunt","year":"2000","unstructured":"Hunt, G.W., Peletier, M.A., Champneys, A.R., Woods, P.D., Wadee, M.A., Budd, C.J., Lord, G.J.: Cellular buckling in long structures. Nonlinear Dyn. 21(1), 3\u201329 (2000)","journal-title":"Nonlinear Dyn."},{"issue":"1","key":"9810_CR33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-018-07882-8","volume":"10","author":"W Jiang","year":"2019","unstructured":"Jiang, W., Huang, H., Liu, F.: A Lieb-like lattice in a covalent-organic framework and its Stoner ferromagnetism. Nat. Commun. 10(1), 1\u20137 (2019)","journal-title":"Nat. Commun."},{"issue":"3","key":"9810_CR34","doi-asserted-by":"publisher","first-page":"1959","DOI":"10.1021\/acs.nanolett.9b05242","volume":"20","author":"W Jiang","year":"2020","unstructured":"Jiang, W., Zhang, S., Wang, Z., Liu, F., Low, T.: Topological band engineering of Lieb lattice in phthalocyanine-based metal\u2013organic frameworks. Nano Lett. 20(3), 1959\u20131966 (2020)","journal-title":"Nano Lett."},{"issue":"1\u20132","key":"9810_CR35","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/S0167-2789(99)00154-2","volume":"136","author":"SL Judd","year":"2000","unstructured":"Judd, S.L., Silber, M.: Simple and superlattice Turing patterns in reaction-diffusion systems: bifurcation, bistability, and parameter collapse. Physica D 136(1\u20132), 45\u201365 (2000)","journal-title":"Physica D"},{"key":"9810_CR36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.045303","volume":"117","author":"A Julku","year":"2016","unstructured":"Julku, A., Peotta, S., Vanhala, T.I., Kim, D.-H., T\u00f6rm\u00e4, P.: Geometric origin of superfluidity in the Lieb-lattice flat band. Phys. Rev. Lett. 117, 045303 (2016)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"9810_CR37","doi-asserted-by":"publisher","first-page":"12204","DOI":"10.1103\/PhysRevE.100.012204","volume":"100","author":"E Knobloch","year":"2019","unstructured":"Knobloch, E., Uecker, H., Wetzel, D.: Defectlike structures and localized patterns in the cubic\u2013quintic-septic Swift\u2013Hohenberg equation. Phys. Rev. E 100(1), 12204 (2019)","journal-title":"Phys. Rev. E"},{"issue":"4","key":"9810_CR38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.044502","volume":"97","author":"G Kozyreff","year":"2006","unstructured":"Kozyreff, G., Chapman, S.J.: Asymptotics of large bound states of localized structures. Phys. Rev. Lett. 97(4), 044502 (2006)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"9810_CR39","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.96.062214","volume":"96","author":"R Kusdiantara","year":"2017","unstructured":"Kusdiantara, R., Susanto, H.: Homoclinic snaking in the discrete Swift\u2013Hohenberg equation. Phys. Rev. E 96(6), 062214 (2017)","journal-title":"Phys. Rev. E"},{"issue":"12","key":"9810_CR40","doi-asserted-by":"publisher","first-page":"5170","DOI":"10.1088\/1361-6544\/ab46e8","volume":"32","author":"R Kusdiantara","year":"2019","unstructured":"Kusdiantara, R., Susanto, H.: Snakes in square, honeycomb and triangular lattices. Nonlinearity 32(12), 5170\u20135190 (2019)","journal-title":"Nonlinearity"},{"issue":"1","key":"9810_CR41","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1137\/S0036139901389495","volume":"63","author":"CR Laing","year":"2001","unstructured":"Laing, C.R., Troy, W.C., Gutkin, B., Ermentrout, G.B.: Multiple bumps in a neuronal model of working memory. SIAM J. Appl. Math. 63(1), 62\u201397 (2001)","journal-title":"SIAM J. Appl. Math."},{"key":"9810_CR42","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.physe.2018.08.019","volume":"105","author":"PT Le","year":"2019","unstructured":"Le, P.T., Yarmohammadi, M.: Impurity-tuning of phase transition and mid-state in 2D spin Lieb lattice. Physica E 105, 56\u201361 (2019)","journal-title":"Physica E"},{"issue":"10","key":"9810_CR43","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1103\/PhysRevLett.62.1201","volume":"62","author":"EH Lieb","year":"1989","unstructured":"Lieb, E.H.: Two theorems on the Hubbard model. Phys. Rev. Lett. 62(10), 1201\u20131204 (1989)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"9810_CR44","doi-asserted-by":"publisher","first-page":"1892","DOI":"10.1137\/18M1225653","volume":"18","author":"DJ Lloyd","year":"2019","unstructured":"Lloyd, D.J.: Invasion fronts outside the homoclinic snaking region in the planar Swift\u2013Hohenberg equation. SIAM J. Appl. Dyn. Syst. 18(4), 1892\u20131933 (2019)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"issue":"2","key":"9810_CR45","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1088\/0951-7715\/22\/2\/013","volume":"22","author":"D Lloyd","year":"2009","unstructured":"Lloyd, D., Sandstede, B.: Localized radial solutions of the Swift\u2013Hohenberg equation. Nonlinearity 22(2), 485 (2009)","journal-title":"Nonlinearity"},{"issue":"3","key":"9810_CR46","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1137\/070707622","volume":"7","author":"DJB Lloyd","year":"2008","unstructured":"Lloyd, D.J.B., Sandstede, B., Avitabile, D., Champneys, A.R.: Localized hexagon patterns of the planar Swift\u2013Hohenberg equation. SIAM J. Appl. Dyn. Syst. 7(3), 1049\u20131100 (2008)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"9810_CR47","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1017\/jfm.2015.565","volume":"783","author":"DJ Lloyd","year":"2015","unstructured":"Lloyd, D.J., Gollwitzer, C., Rehberg, I., Richter, R.: Homoclinic snaking near the surface instability of a polarisable fluid. J. Fluid Mech. 783, 283\u2013305 (2015)","journal-title":"J. Fluid Mech."},{"issue":"6","key":"9810_CR48","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.066207","volume":"84","author":"P Matthews","year":"2011","unstructured":"Matthews, P., Susanto, H.: Variational approximations to homoclinic snaking in continuous and discrete systems. Phys. Rev. E 84(6), 066207 (2011)","journal-title":"Phys. Rev. E"},{"issue":"16","key":"9810_CR49","doi-asserted-by":"publisher","first-page":"1581","DOI":"10.1016\/j.physd.2010.04.004","volume":"239","author":"S McCalla","year":"2010","unstructured":"McCalla, S., Sandstede, B.: Snaking of radial solutions of the multi-dimensional Swift\u2013Hohenberg equation: a numerical study. Physica D 239(16), 1581\u20131592 (2010)","journal-title":"Physica D"},{"issue":"1","key":"9810_CR50","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/srep27397","volume":"6","author":"N McCullen","year":"2016","unstructured":"McCullen, N., Wagenknecht, T.: Pattern formation on networks: from localised activity to Turing patterns. Sci. Rep. 6(1), 1\u20138 (2016)","journal-title":"Sci. Rep."},{"issue":"24","key":"9810_CR51","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.245504","volume":"114","author":"S Mukherjee","year":"2015","unstructured":"Mukherjee, S., Spracklen, A., Choudhury, D., Goldman, N., \u00d6hberg, P., Andersson, E., Thomson, R.R.: Observation of a localized flat-band state in a photonic Lieb lattice. Phys. Rev. Lett. 114(24), 245504 (2015)","journal-title":"Phys. Rev. Lett."},{"issue":"16","key":"9810_CR52","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevB.101.165109","volume":"101","author":"L Oliveira-Lima","year":"2020","unstructured":"Oliveira-Lima, L., Costa, N.C., De Lima, J.P., Scalettar, R.T., Santos, R.R.: Dynamical resilience to disorder: the dilute Hubbard model on the Lieb lattice. Phys. Rev. B 101(16), 1\u20139 (2020)","journal-title":"Phys. Rev. B"},{"issue":"17","key":"9810_CR53","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.118.175301","volume":"118","author":"H Ozawa","year":"2017","unstructured":"Ozawa, H., Taie, S., Ichinose, T., Takahashi, Y.: Interaction-driven shift and distortion of a flat band in an optical Lieb lattice. Phys. Rev. Lett. 118(17), 175301 (2017)","journal-title":"Phys. Rev. Lett."},{"issue":"1\u20133","key":"9810_CR54","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/0167-2789(86)90104-1","volume":"23","author":"Y Pomeau","year":"1986","unstructured":"Pomeau, Y.: Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D 23(1\u20133), 3\u201311 (1986)","journal-title":"Physica D"},{"issue":"1\u20133","key":"9810_CR55","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/0167-2789(96)00077-2","volume":"97","author":"H Sakaguchi","year":"1996","unstructured":"Sakaguchi, H., Brand, H.R.: Stable localized solutions of arbitrary length for the quintic Swift\u2013Hohenberg equation. Physica D 97(1\u20133), 274\u2013285 (1996)","journal-title":"Physica D"},{"issue":"3","key":"9810_CR56","doi-asserted-by":"publisher","first-page":"31102","DOI":"10.1103\/PhysRevE.100.031102","volume":"100","author":"M Salewski","year":"2019","unstructured":"Salewski, M., Gibson, J.F., Schneider, T.M.: Origin of localized snakes-and-ladders solutions of plane Couette flow. Phys. Rev. E 100(3), 31102 (2019)","journal-title":"Phys. Rev. E"},{"issue":"1","key":"9810_CR57","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s42005-021-00548-w","volume":"4","author":"F Scafirimuto","year":"2021","unstructured":"Scafirimuto, F., Urbonas, D., Becker, M.A., Scherf, U., Mahrt, R.F., St\u00f6ferle, T.: Tunable exciton-polariton condensation in a two-dimensional Lieb lattice at room temperature. Commun. Phys. 4(1), 1\u20136 (2021)","journal-title":"Commun. Phys."},{"issue":"3","key":"9810_CR58","doi-asserted-by":"publisher","first-page":"033133","DOI":"10.1063\/1.5135579","volume":"30","author":"H Schmidt","year":"2020","unstructured":"Schmidt, H., Avitabile, D.: Bumps and oscillons in networks of spiking neurons. Chaos 30(3), 033133 (2020)","journal-title":"Chaos"},{"issue":"7","key":"9810_CR59","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1038\/nphys4105","volume":"13","author":"MR Slot","year":"2017","unstructured":"Slot, M.R., Gardenier, T.S., Jacobse, P.H., van Miert, G.C., Kempkes, S.N., Zevenhuizen, S.J., Smith, C.M., Vanmaekelbergh, D., Swart, I.: Experimental realization and characterization of an electronic Lieb lattice. Nat. Phys. 13(7), 672\u2013676 (2017)","journal-title":"Nat. Phys."},{"issue":"1\u20133","key":"9810_CR60","first-page":"232","volume":"274","author":"F Smektala","year":"2010","unstructured":"Smektala, F., Quemard, C., Couderc, V., Barth\u00e9l\u00e9my, A.: Non-linear optical properties of chalcogenide glasses measured by Z-scan. J. Non Cryst. Solids 274(1\u20133), 232\u2013237 (2010)","journal-title":"J. Non Cryst. Solids"},{"issue":"3","key":"9810_CR61","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.035201","volume":"83","author":"H Susanto","year":"2011","unstructured":"Susanto, H., Matthews, P.: Variational approximations to homoclinic snaking. Phys. Rev. E 83(3), 035201 (2011)","journal-title":"Phys. Rev. E"},{"key":"9810_CR62","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.65.085324","volume":"65","author":"H Tamura","year":"2002","unstructured":"Tamura, H., Shiraishi, K., Kimura, T., Takayanagi, H.: Flat-band ferromagnetism in quantum dot superlattices. Phys. Rev. B 65, 085324 (2002)","journal-title":"Phys. Rev. B"},{"issue":"1","key":"9810_CR63","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.physleta.2010.10.010","volume":"375","author":"C Taylor","year":"2010","unstructured":"Taylor, C., Dawes, J.H.: Snaking and isolas of localised states in bistable discrete lattices. Phys. Lett. A 375(1), 14\u201322 (2010)","journal-title":"Phys. Lett. A"},{"key":"9810_CR64","doi-asserted-by":"publisher","first-page":"1530001","DOI":"10.1142\/S0218127415300013","volume":"25","author":"JMT Thompson","year":"2015","unstructured":"Thompson, J.M.T.: Advances in shell buckling: theory and experiments. Int. J. Bifurc. Chaos 25, 1530001 (2015)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"9810_CR65","doi-asserted-by":"crossref","unstructured":"Tian, M., Bramburger, J.J., Sandstede, B.: Snaking bifurcations of localized patterns on ring lattices. arXiv preprint arXiv:2105.02380 (2021)","DOI":"10.1093\/imamat\/hxab023"},{"issue":"5","key":"9810_CR66","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1103\/PhysRevLett.73.640","volume":"73","author":"M Tlidi","year":"1994","unstructured":"Tlidi, M., Mandel, P., Lefever, A.: Localized structures and localized patterns in optical bistability. Phys. Rev. Lett. 73(5), 640 (1994)","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"9810_CR67","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.86.033822","volume":"86","author":"M Tlidi","year":"2012","unstructured":"Tlidi, M., Averlant, E., Vladimirov, A., Panajotov, K.: Delay feedback induces a spontaneous motion of two-dimensional cavity solitons in driven semiconductor microcavities. Phys. Rev. A 86(3), 033822 (2012)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"9810_CR68","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1137\/130918484","volume":"13","author":"H Uecker","year":"2014","unstructured":"Uecker, H., Wetzel, D.: Numerical results for snaking of patterns over patterns in some 2D Selkov\u2013Schnakenberg reaction-diffusion systems. SIAM J. Appl. Dyn. Syst. 13(1), 94\u2013128 (2014)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"9810_CR69","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2020.132383","volume":"406","author":"H Uecker","year":"2020","unstructured":"Uecker, H., Wetzel, D.: Snaking branches of planar BCC fronts in the 3D Brusselator. Physica D 406, 132383 (2020)","journal-title":"Physica D"},{"issue":"4","key":"9810_CR70","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.84.043848","volume":"84","author":"AG Vladimirov","year":"2011","unstructured":"Vladimirov, A.G., Lefever, R., Tlidi, M.: Relative stability of multipeak localized patterns of cavity solitons. Phys. Rev. A 84(4), 043848 (2011)","journal-title":"Phys. Rev. A"},{"key":"9810_CR71","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.146803","volume":"107","author":"YF Wang","year":"2011","unstructured":"Wang, Y.F., Gu, Z.C., Gong, C.D., Sheng, D.N.: Fractional quantum Hall effect of hard-core bosons in topological flat bands. Phys. Rev. Lett. 107, 146803 (2011)","journal-title":"Phys. Rev. Lett."},{"issue":"9","key":"9810_CR72","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.097401","volume":"120","author":"CE Whittaker","year":"2018","unstructured":"Whittaker, C.E., Cancellieri, E., Walker, P.M., Gulevich, D.R., Schomerus, H., Vaitiekus, D., Royall, B., Whittaker, D.M., Clarke, E., Iorsh, I.V., Shelykh, I.A.: Exciton polaritons in a two-dimensional lieb lattice with spin-orbit coupling. Phys. Rev. Lett. 120(9), 097401 (2018)","journal-title":"Phys. Rev. Lett."},{"issue":"3\u20134","key":"9810_CR73","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/S0167-2789(98)00309-1","volume":"129","author":"P Woods","year":"1999","unstructured":"Woods, P., Champneys, A.: Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian Hopf bifurcation. Physica D 129(3\u20134), 147\u2013170 (1999)","journal-title":"Physica D"},{"issue":"2","key":"9810_CR74","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1137\/080734297","volume":"9","author":"AV Yulin","year":"2010","unstructured":"Yulin, A.V., Champneys, A.R.: Discrete snaking: multiple cavity solitons in saturable media. SIAM J. Appl. Dyn. Syst. 9(2), 391\u2013431 (2010)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"issue":"5","key":"9810_CR75","doi-asserted-by":"publisher","first-page":"1341","DOI":"10.3934\/dcdss.2011.4.1341","volume":"4","author":"A Yulin","year":"2011","unstructured":"Yulin, A., Champneys, A.: Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities. Discrete Contin. Dyn. Syst. S 4(5), 1341\u20131357 (2011)","journal-title":"Discrete Contin. Dyn. Syst. S"},{"issue":"1","key":"9810_CR76","doi-asserted-by":"publisher","first-page":"011804(R)","DOI":"10.1103\/PhysRevA.78.011804","volume":"78","author":"AV Yulin","year":"2008","unstructured":"Yulin, A.V., Champneys, A.R., Skryabin, D.V.: Discrete cavity solitons due to saturable nonlinearity. Phys. Rev. A 78(1), 011804(R) (2008)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"9810_CR77","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1364\/JOSAB.19.000369","volume":"19","author":"C Zhan","year":"2002","unstructured":"Zhan, C., Zhang, D., Zhu, D., Wang, D., Li, Y., Li, D., Lu, Z., Zhao, L., Nie, Y.: Third-and fifth-order optical nonlinearities in a new stilbazolium derivative. J. Opt. Soc. Am. B 19(3), 369\u2013375 (2002)","journal-title":"J. Opt. Soc. Am. B"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-022-09810-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-022-09810-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-022-09810-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,23]],"date-time":"2022-10-23T07:03:51Z","timestamp":1666508631000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-022-09810-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,15]]},"references-count":77,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["9810"],"URL":"https:\/\/doi.org\/10.1007\/s00332-022-09810-z","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,15]]},"assertion":[{"value":"19 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"59"}}