{"title":"Lump type solutions: Bäcklund transformation and spectral properties","authors":"Yong Liu , Jun-Cheng Wei , Wen Yang","doi":"10.1016/j.physd.2024.134394","DOIUrl":null,"url":null,"abstract":"<div><div>There are various different ways to obtain traveling waves of lump type(higher order lumps) for the KP-I equation. We propose a general and simple approach to derive them via a Bäcklund transformation. This enables us to establish an explicit connection between those lower energy solutions and higher energy ones. Based on this construction, spectral analysis of the degree 6 solutions is then carried out in details. The analysis of higher energy ones can be done in an inductive way.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134394"},"PeriodicalIF":2.9000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003440","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/10/5 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
There are various different ways to obtain traveling waves of lump type(higher order lumps) for the KP-I equation. We propose a general and simple approach to derive them via a Bäcklund transformation. This enables us to establish an explicit connection between those lower energy solutions and higher energy ones. Based on this construction, spectral analysis of the degree 6 solutions is then carried out in details. The analysis of higher energy ones can be done in an inductive way.
期刊介绍：
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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