{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:28Z","timestamp":1747198048708,"version":"3.40.5"},"reference-count":33,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11901120"],"award-info":[{"award-number":["11901120"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we introduce a first-order low-regularity integrator for the Davey\u2013Stewartson system in the elliptic-elliptic case.\nIt only requires the boundedness of one additional derivative of the solution to be first-order convergent.\nBy rigorous error analysis, we show that the scheme provides first-order accuracy in <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msup>\n                                 <m:mi>H<\/m:mi>\n                                 <m:mi>\u03b3<\/m:mi>\n                              <\/m:msup>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:msup>\n                                    <m:mi mathvariant=\"double-struck\">T<\/m:mi>\n                                    <m:mi>d<\/m:mi>\n                                 <\/m:msup>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0180_ineq_0001.png\"\/>\n                        <jats:tex-math>H^{\\gamma}(\\mathbb{T}^{d})<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> for rough initial data in <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msup>\n                                 <m:mi>H<\/m:mi>\n                                 <m:mrow>\n                                    <m:mi>\u03b3<\/m:mi>\n                                    <m:mo>+<\/m:mo>\n                                    <m:mn>1<\/m:mn>\n                                 <\/m:mrow>\n                              <\/m:msup>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:msup>\n                                    <m:mi mathvariant=\"double-struck\">T<\/m:mi>\n                                    <m:mi>d<\/m:mi>\n                                 <\/m:msup>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0180_ineq_0002.png\"\/>\n                        <jats:tex-math>H^{\\gamma+1}(\\mathbb{T}^{d})<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> with <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>\u03b3<\/m:mi>\n                              <m:mo>&gt;<\/m:mo>\n                              <m:mfrac>\n                                 <m:mi>d<\/m:mi>\n                                 <m:mn>2<\/m:mn>\n                              <\/m:mfrac>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0180_ineq_0003.png\"\/>\n                        <jats:tex-math>\\gamma&gt;\\frac{d}{2}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.<\/jats:p>","DOI":"10.1515\/cmam-2020-0180","type":"journal-article","created":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T12:24:41Z","timestamp":1652271881000},"page":"675-684","source":"Crossref","is-referenced-by-count":1,"title":["Low-Regularity Integrator for the Davey\u2013Stewartson System: Elliptic-Elliptic Case"],"prefix":"10.1515","volume":"22","author":[{"given":"Cui","family":"Ning","sequence":"first","affiliation":[{"name":"School of Financial Mathematics and Statistics , Guangdong University of Finance , Guangzhou , Guangdong 510521 , P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5088-1673","authenticated-orcid":false,"given":"Yaohong","family":"Wang","sequence":"additional","affiliation":[{"name":"Center for Applied Mathematics , Tianjin University , Tianjin , 300072 , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2022,5,12]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"C. Besse,\nSch\u00e9ma de relaxation pour l\u2019\u00e9quation de Schr\u00f6dinger non lin\u00e9aire et les syst\u00e8mes de Davey et Stewartson,\nC. R. Acad. Sci. Paris S\u00e9r. I Math. 326 (1998) no. 12, 1427\u20131432.","key":"2023033112440891041_j_cmam-2020-0180_ref_001","DOI":"10.1016\/S0764-4442(98)80405-9"},{"doi-asserted-by":"crossref","unstructured":"C. Besse, N. J. Mauser and H. P. Stimming,\nNumerical study of the Davey\u2013Stewartson system,\nM2AN Math. Model. Numer. Anal. 38 (2004), no. 6, 1035\u20131054.","key":"2023033112440891041_j_cmam-2020-0180_ref_002","DOI":"10.1051\/m2an:2004049"},{"doi-asserted-by":"crossref","unstructured":"T. Cazenave,\nSemilinear Schr\u00f6dinger Equations,\nCourant Lect. Notes Math. 10,\nAmerican Mathematical Society, Providence, 2003.","key":"2023033112440891041_j_cmam-2020-0180_ref_003","DOI":"10.1090\/cln\/010"},{"doi-asserted-by":"crossref","unstructured":"R. Cipolatti,\nOn the existence of standing waves for a Davey\u2013Stewartson system,\nComm. Partial Differential Equations 17 (1992), no. 5\u20136, 967\u2013988.","key":"2023033112440891041_j_cmam-2020-0180_ref_004","DOI":"10.1080\/03605309208820872"},{"unstructured":"R. Cipolatti,\nOn the instability of ground states for a Davey\u2013Stewartson system,\nAnn. Inst. H. Poincar\u00e9 Phys. Th\u00e9or. 58 (1993), no. 1, 85\u2013104.","key":"2023033112440891041_j_cmam-2020-0180_ref_005"},{"doi-asserted-by":"crossref","unstructured":"A. Davey and K. Stewartson,\nOn three-dimensional packets of surface waves,\nProc. Roy. Soc. Lond. Ser. A 338 (1974), 101\u2013110.","key":"2023033112440891041_j_cmam-2020-0180_ref_006","DOI":"10.1098\/rspa.1974.0076"},{"doi-asserted-by":"crossref","unstructured":"J.-M. Ghidaglia and J.-C. Saut,\nOn the initial value problem for the Davey\u2013Stewartson systems,\nNonlinearity 3 (1990), no. 2, 475\u2013506.","key":"2023033112440891041_j_cmam-2020-0180_ref_007","DOI":"10.1088\/0951-7715\/3\/2\/010"},{"doi-asserted-by":"crossref","unstructured":"N. Hayashi,\nLocal existence in time of solutions to the elliptic-hyperbolic Davey\u2013Stewartson system without smallness condition on the data,\nJ. Anal. Math. 73 (1997), 133\u2013164.","key":"2023033112440891041_j_cmam-2020-0180_ref_008","DOI":"10.1007\/BF02788141"},{"doi-asserted-by":"crossref","unstructured":"N. Hayashi and H. Hirata,\nGlobal existence and asymptotic behaviour in time of small solutions to the elliptic-hyperbolic Davey\u2013Stewartson system,\nNonlinearity 9 (1996), no. 6, 1387\u20131409.","key":"2023033112440891041_j_cmam-2020-0180_ref_009","DOI":"10.1088\/0951-7715\/9\/6\/001"},{"doi-asserted-by":"crossref","unstructured":"N. Hayashi and J.-C. Saut,\nGlobal existence of small solutions to the Davey\u2013Stewartson and the Ishimori systems,\nDifferential Integral Equations 8 (1995), no. 7, 1657\u20131675.","key":"2023033112440891041_j_cmam-2020-0180_ref_010","DOI":"10.57262\/die\/1368397751"},{"doi-asserted-by":"crossref","unstructured":"M. Hofmanov\u00e1 and K. Schratz,\nAn exponential-type integrator for the KdV equation,\nNumer. Math. 136 (2017), no. 4, 1117\u20131137.","key":"2023033112440891041_j_cmam-2020-0180_ref_011","DOI":"10.1007\/s00211-016-0859-1"},{"doi-asserted-by":"crossref","unstructured":"C. Klein, K. McLaughlin and N. Stoilov,\nSpectral approach to the scattering map for the semi-classical defocusing Davey\u2013Stewartson II equation,\nPhys. D 400 (2019), Article ID 132126.","key":"2023033112440891041_j_cmam-2020-0180_ref_012","DOI":"10.1016\/j.physd.2019.05.006"},{"doi-asserted-by":"crossref","unstructured":"C. Klein and N. Stoilov,\nNumerical study of blow-up mechanisms for Davey\u2013Stewartson II systems,\nStud. Appl. Math. 141 (2018), no. 1, 89\u2013112.","key":"2023033112440891041_j_cmam-2020-0180_ref_013","DOI":"10.1111\/sapm.12214"},{"doi-asserted-by":"crossref","unstructured":"C. Klein and N. Stoilov,\nNumerical scattering for the defocusing Davey\u2013Stewartson II equation for initial data with compact support,\nNonlinearity 32 (2019), no. 11, 4258\u20134280.","key":"2023033112440891041_j_cmam-2020-0180_ref_014","DOI":"10.1088\/1361-6544\/ab28c6"},{"doi-asserted-by":"crossref","unstructured":"M. Kn\u00f6ller, A. Ostermann and K. Schratz,\nA Fourier integrator for the cubic nonlinear Schr\u00f6dinger equation with rough initial data,\nSIAM J. Numer. Anal. 57 (2019), no. 4, 1967\u20131986.","key":"2023033112440891041_j_cmam-2020-0180_ref_015","DOI":"10.1137\/18M1198375"},{"doi-asserted-by":"crossref","unstructured":"H. Leblond,\nElectromagnetic waves in ferromagnets: A Davey\u2013Stewartson-type model,\nJ. Phys. A 32 (1999), no. 45, 7907\u20137932.","key":"2023033112440891041_j_cmam-2020-0180_ref_016","DOI":"10.1088\/0305-4470\/32\/45\/308"},{"doi-asserted-by":"crossref","unstructured":"F. Linares and G. Ponce,\nOn the Davey\u2013Stewartson systems,\nAnn. Inst. H. Poincar\u00e9 C Anal. Non Lin\u00e9aire 10 (1993), no. 5, 523\u2013548.","key":"2023033112440891041_j_cmam-2020-0180_ref_017","DOI":"10.1016\/s0294-1449(16)30203-7"},{"doi-asserted-by":"crossref","unstructured":"J. Lu and Y. Wu,\nSharp threshold for scattering of a generalized Davey\u2013Stewartson system in three dimension,\nCommun. Pure Appl. Anal. 14 (2015), no. 5, 1641\u20131670.","key":"2023033112440891041_j_cmam-2020-0180_ref_018","DOI":"10.3934\/cpaa.2015.14.1641"},{"doi-asserted-by":"crossref","unstructured":"G. M. Muslu,\nNumerical study of blow-up to the purely elliptic generalized Davey\u2013Stewartson system,\nJ. Comput. Appl. Math. 317 (2017), 331\u2013342.","key":"2023033112440891041_j_cmam-2020-0180_ref_019","DOI":"10.1016\/j.cam.2016.12.003"},{"doi-asserted-by":"crossref","unstructured":"A. Nachman, I. Regev and D. Tataru,\nA nonlinear Plancherel theorem with applications to global well-posedness for the defocusing Davey\u2013Stewartson equation and to the inverse boundary value problem of Calder\u00f3n,\nInvent. Math. 220 (2020), no. 2, 395\u2013451.","key":"2023033112440891041_j_cmam-2020-0180_ref_020","DOI":"10.1007\/s00222-019-00930-0"},{"unstructured":"A. C. Newell and J. V. Moloney,\nNonlinear Optics,\nAdv. Topics Interdiscip. Math. Sci.,\nAddison-Wesley, Redwood, 1992.","key":"2023033112440891041_j_cmam-2020-0180_ref_021"},{"doi-asserted-by":"crossref","unstructured":"K. Nishinari and J. Satsuma,\nMulti-dimensional localized behavior of electrostatic ion wave in a magnetized plasma,\nPhys. Plasmas 1 (1994), Article ID 2559.","key":"2023033112440891041_j_cmam-2020-0180_ref_022","DOI":"10.1063\/1.870583"},{"unstructured":"M. Ohta,\nInstability of standing waves for the generalized Davey\u2013Stewartson system,\nAnn. Inst. H. Poincar\u00e9 Phys. Th\u00e9or. 62 (1995), no. 1, 69\u201380.","key":"2023033112440891041_j_cmam-2020-0180_ref_023"},{"doi-asserted-by":"crossref","unstructured":"A. Ostermann and K. Schratz,\nLow regularity exponential-type integrators for semilinear Schr\u00f6dinger equations,\nFound. Comput. Math. 18 (2018), no. 3, 731\u2013755.","key":"2023033112440891041_j_cmam-2020-0180_ref_024","DOI":"10.1007\/s10208-017-9352-1"},{"unstructured":"C. Sulem and P.-L. Sulem,\nThe Nonlinear Schr\u00f6dinger Equation, Self-Focusing and Wave Collapse,\nAppl. Math. Sci. 139,\nSpringer, New York, 1999.","key":"2023033112440891041_j_cmam-2020-0180_ref_025"},{"doi-asserted-by":"crossref","unstructured":"M. Tsutsumi,\nDecay of weak solutions to the Davey\u2013Stewartson systems,\nJ. Math. Anal. Appl. 182 (1994), no. 3, 680\u2013704.","key":"2023033112440891041_j_cmam-2020-0180_ref_026","DOI":"10.1006\/jmaa.1994.1113"},{"unstructured":"P. W. White,\nThe Davey\u2013Stewartson equations: A numerical study,\nPh.D. Thesis, Oregon State University, 1994.","key":"2023033112440891041_j_cmam-2020-0180_ref_027"},{"doi-asserted-by":"crossref","unstructured":"P. W. White and J. A. C. Weideman,\nNumerical simulation of solitons and dromions in the Davey\u2013Stewartson system,\nMath. Comput. Simulation 37 (1994), 469\u2013479.","key":"2023033112440891041_j_cmam-2020-0180_ref_028","DOI":"10.1016\/0378-4754(94)00032-8"},{"unstructured":"Y. Wu and F. Yao,\nEmbedded exponential-type low-regularity integrators for KdV equation under rough data, preprint (2020), https:\/\/arxiv.org\/abs\/2008.07053v2.","key":"2023033112440891041_j_cmam-2020-0180_ref_029"},{"doi-asserted-by":"crossref","unstructured":"Y. Wu and X. Zhao,\nOptimal convergence of a second order low-regularity integrator for the KdV equation,\nIMA J. Numer. Anal. (2021), 10.1093\/imanum\/drab054.","key":"2023033112440891041_j_cmam-2020-0180_ref_030","DOI":"10.1093\/imanum\/drab054"},{"doi-asserted-by":"crossref","unstructured":"Y. Wu and X. Zhao,\nEmbedded exponential-type low-regularity integrators for KdV equation under rough data,\nBIT Numer. Math. (2021), 10.1007\/s10543-021-00895-8.","key":"2023033112440891041_j_cmam-2020-0180_ref_031","DOI":"10.1007\/s10543-021-00895-8"},{"doi-asserted-by":"crossref","unstructured":"V. E. Zakharov, S. L. Musher and A. M. Rubenchik,\nHamiltonian approach to the description of nonlinear plasma phenomena,\nPhys. Rep. 129 (1985), no. 5, 285\u2013366.","key":"2023033112440891041_j_cmam-2020-0180_ref_032","DOI":"10.1016\/0370-1573(85)90040-7"},{"doi-asserted-by":"crossref","unstructured":"V. E. Zakharov and E. I. Schulman,\nIntegrability of nonlinear systems and perturbation theory,\nWhat is Integrability?,\nSpringer Ser. Nonlinear Dynam.,\nSpringer, Berlin (1991), 185\u2013250.","key":"2023033112440891041_j_cmam-2020-0180_ref_033","DOI":"10.1007\/978-3-642-88703-1_5"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2020-0180\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2020-0180\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T16:59:30Z","timestamp":1680281970000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2020-0180\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,12]]},"references-count":33,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3,26]]},"published-print":{"date-parts":[[2022,7,1]]}},"alternative-id":["10.1515\/cmam-2020-0180"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2020-0180","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"type":"print","value":"1609-4840"},{"type":"electronic","value":"1609-9389"}],"subject":[],"published":{"date-parts":[[2022,5,12]]}}}