{"title":"On Real Hyperelliptic Solutions of Focusing Modified KdV Equation","authors":"Shigeki Matsutani","doi":"10.1007/s11040-024-09490-z","DOIUrl":null,"url":null,"abstract":"<div><p>We study the real hyperelliptic solutions of the focusing modified KdV (MKdV) equation of genus three. Since the complex hyperelliptic solutions of the focusing MKdV equation over <span>\\({{\\mathbb {C}}}\\)</span> are associated with the real gauged MKdV equation, we present a novel construction related to the real hyperelliptic solutions of the gauged MKdV equation. When the gauge field is constant, it can be regarded as the real solution of the focusing MKdV equation, and thus we also discuss the behavior of the gauge field numerically.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-024-09490-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We study the real hyperelliptic solutions of the focusing modified KdV (MKdV) equation of genus three. Since the complex hyperelliptic solutions of the focusing MKdV equation over \({{\mathbb {C}}}\) are associated with the real gauged MKdV equation, we present a novel construction related to the real hyperelliptic solutions of the gauged MKdV equation. When the gauge field is constant, it can be regarded as the real solution of the focusing MKdV equation, and thus we also discuss the behavior of the gauge field numerically.
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MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas.
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