{"title":"六阶非线性Schrödinger方程的逆散射变换和多孤子解","authors":"Xin Wu, Shou-fu Tian, Jin-Jie Yang","doi":"10.1007/s10255-025-0004-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectral problem are derived directly, and the scattering data with <i>t</i> = 0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions. Then we make use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel’fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basis of that, the multi-soliton solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"536 - 555"},"PeriodicalIF":0.9000,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inverse Scattering Transform and Multi-soliton Solutions for the Sextic Nonlinear Schrödinger Equation\",\"authors\":\"Xin Wu, Shou-fu Tian, Jin-Jie Yang\",\"doi\":\"10.1007/s10255-025-0004-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this work, we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectral problem are derived directly, and the scattering data with <i>t</i> = 0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions. Then we make use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel’fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basis of that, the multi-soliton solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.</p></div>\",\"PeriodicalId\":6951,\"journal\":{\"name\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"volume\":\"41 2\",\"pages\":\"536 - 555\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10255-025-0004-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-025-0004-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Inverse Scattering Transform and Multi-soliton Solutions for the Sextic Nonlinear Schrödinger Equation
In this work, we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectral problem are derived directly, and the scattering data with t = 0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions. Then we make use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel’fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basis of that, the multi-soliton solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.
期刊介绍：
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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