{"title":"Evolution of Nonlinear Periodic Waves in the Focusing and Defocusing Cylindrical Modified Korteweg-de Vries Equations","authors":"Nese Ozdemir, Ali Demirci, Semra Ahmetolan","doi":"10.1007/s10773-024-05841-2","DOIUrl":null,"url":null,"abstract":"<div><p>This study investigates the evolution of dispersive shock wave (DSW) solutions within the focusing and defocusing cylindrical modified Korteweg-de Vries (cmKdV(f)) and (cmKdV(d)) equations under Riemann-type initial conditions. Using Whitham modulation theory, we derive and numerically solve the Whitham systems, enabling a comparison between these asymptotic solutions and direct numerical simulations of the cmKdV equations. The results provide a detailed classification of wave structures in both focusing and defocusing cases of the cmKdV equations. This research offers new insights into the behavior and classification of nonlinear periodic waves in the cmKdV equations.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"63 12","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10773-024-05841-2","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This study investigates the evolution of dispersive shock wave (DSW) solutions within the focusing and defocusing cylindrical modified Korteweg-de Vries (cmKdV(f)) and (cmKdV(d)) equations under Riemann-type initial conditions. Using Whitham modulation theory, we derive and numerically solve the Whitham systems, enabling a comparison between these asymptotic solutions and direct numerical simulations of the cmKdV equations. The results provide a detailed classification of wave structures in both focusing and defocusing cases of the cmKdV equations. This research offers new insights into the behavior and classification of nonlinear periodic waves in the cmKdV equations.
期刊介绍：
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.
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