{"title":"Lax pairs, infinite conservation laws of stochastic potential Korteweg–de Vries equation and their solutions by using Darboux transformation","authors":"Nanda Kanan Pal, Prasanta Chatterjee, Abdul-Majid Wazwaz, Santanu Raut","doi":"10.1007/s12043-024-02856-6","DOIUrl":null,"url":null,"abstract":"<div><p>This article carried out the Lax pairs and infinite conservation laws of the stochastic potential Korteweg–de Vries (spKdV) equation, which claims its integrability in the Lax pair sense. The infinite conservation laws of the spKdV equation were established using its Lax pair. The Darboux transformation was conducted and several pertinent theorems and propositions were briefly discussed for deriving especially the complexiton-type solutions. Some complicated efficient solutions, such as higher-order positon, negaton, hybrid positon-rational solution and negaton-rational solutions were explored from the spKdV equation by choosing initial trivial seed solutions.\n</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"99 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pramana","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s12043-024-02856-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This article carried out the Lax pairs and infinite conservation laws of the stochastic potential Korteweg–de Vries (spKdV) equation, which claims its integrability in the Lax pair sense. The infinite conservation laws of the spKdV equation were established using its Lax pair. The Darboux transformation was conducted and several pertinent theorems and propositions were briefly discussed for deriving especially the complexiton-type solutions. Some complicated efficient solutions, such as higher-order positon, negaton, hybrid positon-rational solution and negaton-rational solutions were explored from the spKdV equation by choosing initial trivial seed solutions.
期刊介绍：
Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
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