{"title":"Painlevé analysis of the resonant third-order nonlinear Schrödinger equation","authors":"","doi":"10.1016/j.aml.2024.109232","DOIUrl":null,"url":null,"abstract":"<div><p>The resonant Schrödinger equation of the third order is studied. The Painlevé test for nonlinear partial differential equations is used to determine integrability of equation. It is shown that the necessary condition for integrability of partial differential equations by the inverse scattering transform is fulfilled at certain parameter restriction. Analytical solutions in the form of periodic and solitary wave are presented.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002520","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The resonant Schrödinger equation of the third order is studied. The Painlevé test for nonlinear partial differential equations is used to determine integrability of equation. It is shown that the necessary condition for integrability of partial differential equations by the inverse scattering transform is fulfilled at certain parameter restriction. Analytical solutions in the form of periodic and solitary wave are presented.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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