{"title":"Symmetries, travelling-wave and self-similar solutions of two-component BKP hierarchy","authors":"J. Mohammed Zubair Ahamed, R. Sinuvasan","doi":"10.1016/j.aej.2024.10.063","DOIUrl":null,"url":null,"abstract":"<div><div>We investigate the two-component BKP hierarchy equation for its Lie point symmetries. To obtain a complete classification of the group-invariant solution, we derive the one-dimensional optimal system of subalgebras of <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>D</mi><msub><mrow><mo>⨂</mo></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>. By employing those subalgebras, we construct the invariant solutions which are represented through Weierstrass elliptic functions, Jacobi elliptic functions, and soliton solutions. Also, we analyse the existence of a bounded travelling-wave solution for the equation. Moreover, through the utilization of scale-invariant symmetry, we derive a self-similar solution. Additionally, by conducting singularity analysis, the solution can be expressed in the form of a right Painlevè series.</div></div>","PeriodicalId":7484,"journal":{"name":"alexandria engineering journal","volume":"111 ","pages":"Pages 601-609"},"PeriodicalIF":6.8000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"alexandria engineering journal","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1110016824012201","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the two-component BKP hierarchy equation for its Lie point symmetries. To obtain a complete classification of the group-invariant solution, we derive the one-dimensional optimal system of subalgebras of . By employing those subalgebras, we construct the invariant solutions which are represented through Weierstrass elliptic functions, Jacobi elliptic functions, and soliton solutions. Also, we analyse the existence of a bounded travelling-wave solution for the equation. Moreover, through the utilization of scale-invariant symmetry, we derive a self-similar solution. Additionally, by conducting singularity analysis, the solution can be expressed in the form of a right Painlevè series.
期刊介绍：
Alexandria Engineering Journal is an international journal devoted to publishing high quality papers in the field of engineering and applied science. Alexandria Engineering Journal is cited in the Engineering Information Services (EIS) and the Chemical Abstracts (CA). The papers published in Alexandria Engineering Journal are grouped into five sections, according to the following classification:
• Mechanical, Production, Marine and Textile Engineering
• Electrical Engineering, Computer Science and Nuclear Engineering
• Civil and Architecture Engineering
• Chemical Engineering and Applied Sciences
• Environmental Engineering
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