{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:03:54Z","timestamp":1770980634888,"version":"3.50.1"},"reference-count":57,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T00:00:00Z","timestamp":1768608000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T00:00:00Z","timestamp":1768608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012165","name":"Key Technologies Research and Development Program","doi-asserted-by":"publisher","award":["2024YFE03240400"],"award-info":[{"award-number":["2024YFE03240400"]}],"id":[{"id":"10.13039\/501100012165","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42450275"],"award-info":[{"award-number":["42450275"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271413"],"award-info":[{"award-number":["12271413"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12401308"],"award-info":[{"award-number":["12401308"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s10915-026-03180-4","type":"journal-article","created":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T17:53:59Z","timestamp":1768672439000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Second Order Gauge-Transformed Exponential Integrators for gKdV Equations with Rough Data: Convergence and Application"],"prefix":"10.1007","volume":"106","author":[{"given":"Bing","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qianrui","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-6057-2627","authenticated-orcid":false,"given":"Xiaofei","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,17]]},"reference":[{"issue":"6","key":"3180_CR1","doi-asserted-by":"publisher","first-page":"3648","DOI":"10.1093\/imanum\/drad093","volume":"44","author":"Y Alama Bronsard","year":"2024","unstructured":"Alama Bronsard, Y.: A symmetric low-regularity integrator for the nonlinear Schr\u00f6dinger equation. IMA J. Numer. Anal. 44(6), 3648\u20133682 (2024)","journal-title":"IMA J. Numer. Anal."},{"key":"3180_CR2","unstructured":"Alama\u00a0Bronsard, Y., Bruned, Y., Maierhofer, G., Schratz, K.: Symmetric resonance based integrators and forest formulae. arXiv:2305.16737 (2023)"},{"key":"3180_CR3","doi-asserted-by":"publisher","first-page":"1797","DOI":"10.1512\/iumj.2017.66.6135","volume":"66","author":"J Bao","year":"2017","unstructured":"Bao, J., Wu, Y.: Global well-posedness for the periodic generalized Korteweg-de Vries equation. Indiana Univ. Math. J. 66, 1797\u20131825 (2017)","journal-title":"Indiana Univ. Math. J."},{"issue":"283","key":"3180_CR4","doi-asserted-by":"publisher","first-page":"1401","DOI":"10.1090\/S0025-5718-2013-02661-0","volume":"82","author":"J Bona","year":"2013","unstructured":"Bona, J., Chen, H., Karakashian, O., Xing, Y.: Conservative, discontinuous Galerkin methods for the generalized Korteweg-de Vries equation. Math. Comput. 82(283), 1401\u20131432 (2013)","journal-title":"Math. Comput."},{"issue":"7","key":"3180_CR5","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1016\/0898-1221(86)90031-3","volume":"12","author":"J Bona","year":"1986","unstructured":"Bona, J., Dougalis, V., Karakashian, O.: Fully discrete Galerkin methods for the Korteweg-de Vries equation. Comput. Math. Appl. 12(7), 859\u2013884 (1986)","journal-title":"Comput. Math. Appl."},{"issue":"1695","key":"3180_CR6","first-page":"107","volume":"351","author":"J Bona","year":"1995","unstructured":"Bona, J., Dougalis, V., Karakashian, O., McKinney, W.: Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 351(1695), 107\u2013164 (1995)","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"issue":"000","key":"3180_CR7","first-page":"76","volume":"10","author":"Y Bruned","year":"2022","unstructured":"Bruned, Y., Schratz, K.: Resonance-based schemes for dispersive equations via decorated trees. Forum Math. Pi 10(000), 76 (2022)","journal-title":"Forum Math. Pi"},{"issue":"3","key":"3180_CR8","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1093\/imanum\/drad017","volume":"44","author":"J Cao","year":"2024","unstructured":"Cao, J., Li, B., Lin, Y.: A new second-order low-regularity integrator for the cubic nonlinear Schr\u00f6dinger equation. IMA J. Numer. Anal. 44(3), 1313\u20131345 (2024)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"3180_CR9","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1137\/24M1635879","volume":"63","author":"J Cao","year":"2025","unstructured":"Cao, J., Li, B., Lin, Y., Yao, F.: Numerical approximation of discontinuous solutions of the semilinear wave equation. SIAM J. Numer. Anal. 63(1), 214\u2013238 (2025)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"3180_CR10","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1002\/cpa.20277","volume":"63","author":"T Claeys","year":"2010","unstructured":"Claeys, T., Grava, T.: Painlev\u00e9 II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit. Commun. Pure Appl. Math. 63(2), 203\u2013232 (2010)","journal-title":"Commun. Pure Appl. Math."},{"issue":"3","key":"3180_CR11","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1090\/S0894-0347-03-00421-1","volume":"16","author":"J Colliander","year":"2003","unstructured":"Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T.: Sharp global well-posedness for KdV and modified KdV on $$\\mathbb{R} $$ and $$\\mathbb{T} $$. J. Am. Math. Soc. 16(3), 705\u2013749 (2003)","journal-title":"J. Am. Math. Soc."},{"issue":"1","key":"3180_CR12","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/S0022-1236(03)00218-0","volume":"211","author":"J Colliander","year":"2004","unstructured":"Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T.: Multilinear estimates for periodic KdV equations, and applications. J. Funct. Anal. 211(1), 173\u2013218 (2004)","journal-title":"J. Funct. Anal."},{"issue":"1","key":"3180_CR13","doi-asserted-by":"publisher","first-page":"628","DOI":"10.1093\/imanum\/dry082","volume":"40","author":"C Court\u00e8s","year":"2020","unstructured":"Court\u00e8s, C., Lagouti\u00e8re, F., Rousset, F.: Error estimates of finite difference schemes for the Korteweg-de Vries equation. IMA J. Numer. Anal. 40(1), 628\u2013685 (2020)","journal-title":"IMA J. Numer. Anal."},{"key":"3180_CR14","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.physd.2016.04.006","volume":"333","author":"G El","year":"2016","unstructured":"El, G., Hoefer, M.: Dispersive shock waves and modulation theory. Phys. D: Nonlinear Phenom. 333, 11\u201365 (2016)","journal-title":"Phys. D: Nonlinear Phenom."},{"issue":"1","key":"3180_CR15","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/15M1015650","volume":"59","author":"G El","year":"2017","unstructured":"El, G., Hoefer, M., Shearer, M.: Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws. SIAM Rev. 59(1), 3\u201361 (2017)","journal-title":"SIAM Rev."},{"key":"3180_CR16","doi-asserted-by":"crossref","unstructured":"Feng, Y., Maierhofer, G., Wang, C.: Explicit symmetric low-regularity integrators for the nonlinear Schr\u00f6dinger equation. arXiv:2411.07720 (2024)","DOI":"10.1137\/24M1708723"},{"issue":"19","key":"3180_CR17","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1103\/PhysRevLett.19.1095","volume":"19","author":"C Gardner","year":"1967","unstructured":"Gardner, C., Greene, J., Kruskal, M., Miura, R.: Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19(19), 1095 (1967)","journal-title":"Phys. Rev. Lett."},{"key":"3180_CR18","doi-asserted-by":"crossref","unstructured":"Gardner, C., Greene, J., Kruskal, M., Miura, R.: The Korteweg-de Vries equation and generalizations. VI. Method for exact solutions. Commun. Pure Appl. Math. 27(1), 97\u2013133 (1974)","DOI":"10.1002\/cpa.3160270108"},{"issue":"23\u201324","key":"3180_CR19","doi-asserted-by":"publisher","first-page":"2246","DOI":"10.1016\/j.physd.2012.04.001","volume":"241","author":"T Grava","year":"2012","unstructured":"Grava, T., Klein, C.: A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions. Phys. D: Nonlinear Phenom. 241(23\u201324), 2246\u20132264 (2012)","journal-title":"Phys. D: Nonlinear Phenom."},{"issue":"12","key":"3180_CR20","doi-asserted-by":"publisher","first-page":"1569","DOI":"10.1002\/cpa.10050","volume":"55","author":"T Grava","year":"2002","unstructured":"Grava, T., Tian, F.: The generation, propagation, and extinction of multiphases in the KdV zero-dispersion limit. Commun. Pure Appl. Math. 55(12), 1569\u20131639 (2002)","journal-title":"Commun. Pure Appl. Math."},{"key":"3180_CR21","first-page":"291","volume":"38","author":"A Gurevich","year":"1974","unstructured":"Gurevich, A., Pitayevsky, L.: Nonstationary structure of a collisionless shock wave. J. Exp. Theor. Phys. 38, 291\u2013297 (1974)","journal-title":"J. Exp. Theor. Phys."},{"key":"3180_CR22","volume-title":"Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations","author":"E Hairer","year":"2006","unstructured":"Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. Springer, Berlin (2006)"},{"key":"3180_CR23","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1017\/S0962492910000048","volume":"19","author":"M Hochbruck","year":"2010","unstructured":"Hochbruck, M., Ostermann, A.: Exponential integrators. Acta Numer 19, 209\u2013286 (2010)","journal-title":"Acta Numer"},{"issue":"4","key":"3180_CR24","doi-asserted-by":"publisher","first-page":"1117","DOI":"10.1007\/s00211-016-0859-1","volume":"136","author":"M Hofmanov\u00e1","year":"2017","unstructured":"Hofmanov\u00e1, M., Schratz, K.: An exponential-type integrator for the KdV equation. Numer. Math. 136(4), 1117\u20131137 (2017)","journal-title":"Numer. Math."},{"issue":"1","key":"3180_CR25","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1006\/jcph.1999.6273","volume":"153","author":"H Holden","year":"1999","unstructured":"Holden, H., Karlsen, K., Risebro, N.: Operator splitting methods for generalized Korteweg-de Vries equations. J. Comput. Phys. 153(1), 203\u2013222 (1999)","journal-title":"J. Comput. Phys."},{"issue":"274","key":"3180_CR26","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1090\/S0025-5718-2010-02402-0","volume":"80","author":"H Holden","year":"2011","unstructured":"Holden, H., Karlsen, K., Risebro, N., Tao, T.: Operator splitting for the KdV equation. Math. Comput. 80(274), 821\u2013846 (2011)","journal-title":"Math. Comput."},{"issue":"281","key":"3180_CR27","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1090\/S0025-5718-2012-02624-X","volume":"82","author":"H Holden","year":"2013","unstructured":"Holden, H., Lubich, C., Risebro, N.: Operator splitting for partial differential equations with Burgers nonlinearity. Math. Comput. 82(281), 173\u2013185 (2013)","journal-title":"Math. Comput."},{"key":"3180_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2024.109180","volume":"300","author":"X Hong","year":"2024","unstructured":"Hong, X., Wei, Q., Zhao, X.: Comparison of different discontinuous Galerkin methods based on various reformulations for gKdV equation: Soliton dynamics and blowup. Comput. Phys. Comm. 300, 109180 (2024)","journal-title":"Comput. Phys. Comm."},{"issue":"7","key":"3180_CR29","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1002\/cpa.3160410704","volume":"41","author":"T Kato","year":"1988","unstructured":"Kato, T., Ponce, G.: Commutator estimates and the Euler and Navier-Stokes equations. Commun. Pure Appl. Math. 41(7), 891\u2013907 (1988)","journal-title":"Commun. Pure Appl. Math."},{"issue":"1","key":"3180_CR30","doi-asserted-by":"publisher","first-page":"249","DOI":"10.4007\/annals.2019.190.1.4","volume":"190","author":"R Killip","year":"2019","unstructured":"Killip, R., Vi\u015fan, M.: KdV is well-posed in $${H}^{-1}$$. Ann. Math. 190(1), 249\u2013305 (2019)","journal-title":"Ann. Math."},{"issue":"116\u2013135","key":"3180_CR31","first-page":"37","volume":"29","author":"C Klein","year":"2008","unstructured":"Klein, C.: Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schr\u00f6dinger equation. Electron. Trans. Numer. Anal. 29(116\u2013135), 37 (2008)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"3180_CR32","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.physd.2015.04.003","volume":"304","author":"C Klein","year":"2015","unstructured":"Klein, C., Peter, R.: Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg-de Vries equations. Phys. D: Nonlinear Phenom. 304, 52\u201378 (2015)","journal-title":"Phys. D: Nonlinear Phenom."},{"key":"3180_CR33","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1080\/14786449508620739","volume":"39","author":"D Korteweg","year":"1895","unstructured":"Korteweg, D., de Vries, G.: On the change of form of long waves advancing in a rectangular channel, and a new type of long stationary wave. Philos. Mag. 39, 422\u2013443 (1895)","journal-title":"Philos. Mag."},{"key":"3180_CR34","doi-asserted-by":"crossref","unstructured":"Lax, P., Levermore, C.: The small dispersion limit of the Korteweg-de Vries equation, I, II, III. Commun. Pure Appl. Math. 36(3) (1983)","DOI":"10.1002\/cpa.3160360302"},{"issue":"1","key":"3180_CR35","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s00211-021-01226-3","volume":"149","author":"B Li","year":"2021","unstructured":"Li, B., Wu, Y.: A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schr\u00f6dinger equation. Numer. Math. 149(1), 151\u2013183 (2021)","journal-title":"Numer. Math."},{"key":"3180_CR36","doi-asserted-by":"crossref","unstructured":"Li, B., Wu, Y.: An unfiltered low-regularity integrator for the KdV equation with solutions below $${H^1}$$. Found. Comput. Math. (2025)","DOI":"10.1007\/s10208-025-09702-0"},{"issue":"4","key":"3180_CR37","doi-asserted-by":"publisher","first-page":"1689","DOI":"10.1137\/22M1530501","volume":"61","author":"B Li","year":"2023","unstructured":"Li, B., Wu, Y., Zhao, X.: Gauge-transformed exponential integrator for generalized KdV equations with rough data. SIAM J. Numer. Anal. 61(4), 1689\u20131715 (2023)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"3180_CR38","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.jcp.2005.10.016","volume":"215","author":"H Liu","year":"2006","unstructured":"Liu, H., Yan, J.: A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. J. Comput. Phys. 215(1), 197\u2013218 (2006)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"3180_CR39","doi-asserted-by":"publisher","first-page":"1380","DOI":"10.1137\/S0036142900378327","volume":"39","author":"H Ma","year":"2001","unstructured":"Ma, H., Sun, W.: Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation. SIAM J. Numer. Anal. 39(4), 1380\u20131394 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"3180_CR40","unstructured":"Maierhofer, G., Schratz, K.: Bridging the gap: symplecticity and low regularity in Runge-Kutta resonance-based schemes. arXiv:2205.05024 (2022)"},{"key":"3180_CR41","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s11005-013-0605-x","volume":"103","author":"D Masoero","year":"2013","unstructured":"Masoero, D., Raimondo, A.: Semiclassical limit for generalized KdV equations before the gradient catastrophe. Lett. Math. Phys. 103, 559\u2013583 (2013)","journal-title":"Lett. Math. Phys."},{"issue":"3","key":"3180_CR42","doi-asserted-by":"publisher","first-page":"488","DOI":"10.1137\/0514042","volume":"14","author":"J McLeod","year":"1983","unstructured":"McLeod, J., Olver, P.: The connection between partial differential equations soluble by inverse scattering and ordinary differential equations of painlev\u00e9 type. SIAM J. Math. Anal. 14(3), 488\u2013506 (1983)","journal-title":"SIAM J. Math. Anal."},{"issue":"8","key":"3180_CR43","doi-asserted-by":"publisher","first-page":"1202","DOI":"10.1063\/1.1664700","volume":"9","author":"R Miura","year":"1968","unstructured":"Miura, R.: Korteweg-de vries equation and generalizations. I. A remarkable explicit nonlinear transformation. J. Math. Phys. 9(8), 1202\u20131204 (1968)","journal-title":"J. Math. Phys."},{"issue":"3","key":"3180_CR44","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1137\/1018076","volume":"18","author":"R Miura","year":"1976","unstructured":"Miura, R.: The Korteweg-de Vries equation: a survey of results. SIAM Rev. 18(3), 412\u2013459 (1976)","journal-title":"SIAM Rev."},{"issue":"3","key":"3180_CR45","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1137\/21M1408166","volume":"60","author":"C Ning","year":"2022","unstructured":"Ning, C., Wu, Y., Zhao, X.: An embedded exponential-type low-regularity integrator for mKdV equation. SIAM J. Numer. Anal. 60(3), 999\u20131025 (2022)","journal-title":"SIAM J. Numer. Anal."},{"key":"3180_CR46","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1007\/s10208-017-9352-1","volume":"18","author":"A Ostermann","year":"2018","unstructured":"Ostermann, A., Schratz, K.: Low regularity exponential-type integrators for semilinear Schr\u00f6dinger equations. Found. Comput. Math. 18, 731\u2013755 (2018)","journal-title":"Found. Comput. Math."},{"key":"3180_CR47","doi-asserted-by":"publisher","first-page":"127","DOI":"10.2140\/paa.2022.4.127","volume":"4","author":"F Rousset","year":"2022","unstructured":"Rousset, F., Schratz, K.: Convergence error estimates at low regularity for time discretizations of KdV. Pure Appl. Anal. 4, 127\u2013152 (2022)","journal-title":"Pure Appl. Anal."},{"issue":"5","key":"3180_CR48","doi-asserted-by":"publisher","first-page":"1595","DOI":"10.1137\/S0036142902410271","volume":"41","author":"J Shen","year":"2003","unstructured":"Shen, J.: A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: application to the KdV equation. SIAM J. Numer. Anal. 41(5), 1595\u20131619 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"3180_CR49","doi-asserted-by":"crossref","unstructured":"Staffilani, G.: On solutions for periodic generalized KdV equations. Int. Math. Res. Not. 1997(18) (1997)","DOI":"10.1155\/S1073792897000585"},{"key":"3180_CR50","unstructured":"Tao, T.: Nonlinear dispersive equations: local and global analysis. 106. American Mathematical Society, Providence (2006)"},{"key":"3180_CR51","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719598","volume-title":"Spectral methods in MATLAB","author":"L Trefethen","year":"2000","unstructured":"Trefethen, L.: Spectral methods in MATLAB. SIAM, Philadelphia (2000)"},{"issue":"3","key":"3180_CR52","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1002\/cpa.3160430303","volume":"43","author":"S Venakides","year":"1990","unstructured":"Venakides, S.: The Korteweg-de Vries equation with small dispersion: higher order Lax-Levermore theory. Commun. Pure Appl. Math. 43(3), 335\u2013361 (1990)","journal-title":"Commun. Pure Appl. Math."},{"issue":"337","key":"3180_CR53","doi-asserted-by":"publisher","first-page":"2215","DOI":"10.1090\/mcom\/3751","volume":"91","author":"Y Wang","year":"2022","unstructured":"Wang, Y., Zhao, X.: A symmetric low-regularity integrator for nonlinear Klein-Gordon equation. Math. Comput. 91(337), 2215\u20132245 (2022)","journal-title":"Math. Comput."},{"issue":"3","key":"3180_CR54","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1007\/s10543-021-00895-8","volume":"62","author":"Y Wu","year":"2022","unstructured":"Wu, Y., Zhao, X.: Embedded exponential-type low-regularity integrators for KdV equation under rough data. BIT Numer. Math. 62(3), 1049\u20131090 (2022)","journal-title":"BIT Numer. Math."},{"key":"3180_CR55","doi-asserted-by":"publisher","first-page":"3499","DOI":"10.1093\/imanum\/drab054","volume":"42","author":"Y Wu","year":"2022","unstructured":"Wu, Y., Zhao, X.: Optimal convergence of a first order low-regularity integrator for the KdV equation. IMA J. Numer. Anal. 42, 3499\u20133528 (2022)","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"3180_CR56","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1137\/S0036142901390378","volume":"40","author":"J Yan","year":"2002","unstructured":"Yan, J., Shu, C.: A local discontinuous Galerkin method for KdV type equations. SIAM J. Numer. Anal. 40(2), 769\u2013791 (2002)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"3180_CR57","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1103\/PhysRevLett.15.240","volume":"15","author":"N Zabusky","year":"1965","unstructured":"Zabusky, N., Kruskal, M.: Interaction of \u201csolitons\u2019\u2019 in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15(6), 240 (1965)","journal-title":"Phys. Rev. Lett."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03180-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-026-03180-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03180-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T10:04:21Z","timestamp":1770977061000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-026-03180-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,17]]},"references-count":57,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["3180"],"URL":"https:\/\/doi.org\/10.1007\/s10915-026-03180-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,17]]},"assertion":[{"value":"6 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 December 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 December 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 January 2026","order":4,"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":"Conflicts of Interest"}}],"article-number":"50"}}