{"title":"Nonlocal ∂̄ formalism for the three-spatial-dimensions Kaup–Kuperschmidt equation with two temporal variables","authors":"Huanhuan Lu , Yufeng Zhang","doi":"10.1016/j.aml.2024.109404","DOIUrl":null,"url":null,"abstract":"<div><div>By complexifying the independent variables of the Kaup–Kuperschmidt (KK) equation, we derive the 4+2 integrable extension of the KK equation and its Lax pair. The construction of the associated nonlinear Fourier transform pair comprising both direct and inverse transforms is accomplished by conducting a spectral analysis of the <span><math><mi>t</mi></math></span>-independent part of the Lax pair. In the final section, the nonlinear Fourier transform pair will be used, after also taking into account the appropriate time evolution, for solving the Cauchy initial value problem of the three-spatial-dimensions KK equation with two temporal variables.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109404"},"PeriodicalIF":2.9000,"publicationDate":"2024-11-28","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/S0893965924004245","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
By complexifying the independent variables of the Kaup–Kuperschmidt (KK) equation, we derive the 4+2 integrable extension of the KK equation and its Lax pair. The construction of the associated nonlinear Fourier transform pair comprising both direct and inverse transforms is accomplished by conducting a spectral analysis of the -independent part of the Lax pair. In the final section, the nonlinear Fourier transform pair will be used, after also taking into account the appropriate time evolution, for solving the Cauchy initial value problem of the three-spatial-dimensions KK equation with two temporal variables.
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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