{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T19:57:34Z","timestamp":1790798254612,"version":"4.1.0"},"reference-count":24,"publisher":"Optica Publishing Group","issue":"19","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"National Natural Science Foundation of\n\t\t\t\t\t\tChina","award":["12265015"],"award-info":[{"award-number":["12265015"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Lett."],"published-print":{"date-parts":[[2026,10,1]]},"abstract":"<jats:p>This paper investigates soliton families in the two-dimensional Kerr\n\t\t\t\t\tnonlinear Schr\u00f6dinger equation with a complex linear lattice. Two\n\t\t\t\t\tkinds of complex lattices are considered, both consisting of square\n\t\t\t\t\tunit cells and each compatible with more than one spatial symmetry.\n\t\t\t\t\tThe first complex lattice exhibits one parity-time (PT) symmetry and\n\t\t\t\t\tone partial PT (PPT) symmetry, whereas the second one possesses double\n\t\t\t\t\tPPT symmetry. The band structures and linearized spectra of these two\n\t\t\t\t\tlattices display significant differences. In the presence of\n\t\t\t\t\tself-focusing nonlinearity, multiple types of solitons are found\n\t\t\t\t\twithin the semi-infinite band gaps. The stability of these localized\n\t\t\t\t\tgap modes is examined using two numerical approaches: linear stability\n\t\t\t\t\tanalysis and direct perturbed simulations. The results indicate that\n\t\t\t\t\tall solitons possess stable regions within the first complex square\n\t\t\t\t\tlattice, whereas they are all unstable in the second complex lattice.\n\t\t\t\t\tThis instability is attributed to the more intricate imaginary part,\n\t\t\t\t\tleading to the appearance of nonzero real parts in their stability\n\t\t\t\t\teigenvalue spectra.<\/jats:p>","DOI":"10.1364\/ol.612938","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T13:00:08Z","timestamp":1789390808000},"page":"5593","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Soliton families in the complex square lattice with double spatial symmetry"],"prefix":"10.1364","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7014-6660","authenticated-orcid":true,"given":"Jianwen","family":"Wu","sequence":"first","affiliation":[{"name":"Quzhou University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dumitru","family":"Mihalache","sequence":"additional","affiliation":[{"name":"Horia Hulubei National Institute of Physics and Nuclear Engineering"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Milivoj R.","family":"Beli\u0107","sequence":"additional","affiliation":[{"name":"Hamad Bin Khalifa University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3607-594X","authenticated-orcid":true,"given":"Qing","family":"Wang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0066vpg85","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"ol-51-19-5593-R1","doi-asserted-by":"publisher","first-page":"103904","DOI":"10.1103\/PhysRevLett.100.103904","type":"journal-article","volume":"100","author":"Makris","year":"2008","journal-title":"Phys. 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All rights, including\n\t\t\t\t\tfor text and data mining (TDM), Artificial Intelligence (AI) training,\n\t\t\t\t\tand similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}