{"title":"A novel class of soliton solutions and conservation laws of the generalised BS equation by Lie symmetry method","authors":"Dig vijay Tanwar, Raj Kumar","doi":"10.1007/s12043-024-02796-1","DOIUrl":null,"url":null,"abstract":"<div><p>The interaction between a Riemann wave propagating along the <i>y</i>-axis and a long wave along the <i>x</i>-axis results in a generalised breaking soliton (gBS) equation. Lie symmetries of the equation are generated in this article to derive some rarely available classes of invariant solutions. The presence of arbitrary functions in each solution opens up a broad class of solution profiles. 3D profiles are used to explore more properties of the solutions to the gBS equation. The profiles describe doubly solitons, annihilation of parabolic, periodic solitons, line solitons and solitons on curved surface types. Solution profiles are useful in optical fibre, acoustic waves in a crystal lattice, long waves in stratified oceans, long-distance transmission and shallow water waves. The Lie symmetry approach has future scope to provide more variety in solutions due to the capability of solutions to include functions and arbitrary constants. This research effectively demonstrates the uniqueness of the solutions when compared with the previously published result. Moreover, the adjoint equation and conserved vectors are determined using Noether’s theorem.\n</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"98 3","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-08-10","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/s12043-024-02796-1","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
The interaction between a Riemann wave propagating along the y-axis and a long wave along the x-axis results in a generalised breaking soliton (gBS) equation. Lie symmetries of the equation are generated in this article to derive some rarely available classes of invariant solutions. The presence of arbitrary functions in each solution opens up a broad class of solution profiles. 3D profiles are used to explore more properties of the solutions to the gBS equation. The profiles describe doubly solitons, annihilation of parabolic, periodic solitons, line solitons and solitons on curved surface types. Solution profiles are useful in optical fibre, acoustic waves in a crystal lattice, long waves in stratified oceans, long-distance transmission and shallow water waves. The Lie symmetry approach has future scope to provide more variety in solutions due to the capability of solutions to include functions and arbitrary constants. This research effectively demonstrates the uniqueness of the solutions when compared with the previously published result. Moreover, the adjoint equation and conserved vectors are determined using Noether’s theorem.
沿 y 轴传播的黎曼波与沿 x 轴传播的长波之间的相互作用产生了广义破缺孤子(gBS)方程。本文利用该方程的列对称性,推导出一些罕见的不变解类。每个解中任意函数的存在开辟了一类广泛的解剖面。三维剖面用于探索 gBS 方程解的更多特性。这些剖面描述了双孤子、抛物线湮灭、周期孤子、线孤子和弯曲表面类型的孤子。解剖面对光纤、晶格中的声波、分层海洋中的长波、长距离传输和浅水波等都很有用。由于解法可以包含函数和任意常数,因此李对称方法未来有可能提供更多样的解法。与之前发表的结果相比,这项研究有效地证明了解的唯一性。此外,还利用诺特定理确定了邻接方程和守恒向量。
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.