Raj Kumar , Ravi Shankar Verma , Atul Kumar Tiwari
{"title":"(2+1)-色散长波方程的相似解","authors":"Raj Kumar , Ravi Shankar Verma , Atul Kumar Tiwari","doi":"10.1016/j.joes.2021.12.005","DOIUrl":null,"url":null,"abstract":"<div><p>This work is devoted to get a new family of analytical solutions of the (2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth, and can be observed in an open sea or in wide channels. The solutions are obtained by using the invariance property of the similarity transformations method <em>via</em> one-parameter Lie group theory. The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs. Under adequate restrictions, the reduced system of ODEs is solved. Numerical simulation is performed to describe the solutions in a physically meaningful way. The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein. In each animation, a frame for dominated behavior is captured. They exhibit elastic multisolitons, single soliton, doubly solitons, stationary, kink and parabolic nature. The results are significant since these have confirmed some of the established results of S. Kumar et al. (2020) and K. Sharma et al. (2020). Some of their solutions can be deduced from the results derived in this work. Other results in the existing literature are different from those in this work.</p></div>","PeriodicalId":48514,"journal":{"name":"Journal of Ocean Engineering and Science","volume":"8 2","pages":"Pages 111-123"},"PeriodicalIF":13.0000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"On similarity solutions to (2+1)-dispersive long-wave equations\",\"authors\":\"Raj Kumar , Ravi Shankar Verma , Atul Kumar Tiwari\",\"doi\":\"10.1016/j.joes.2021.12.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This work is devoted to get a new family of analytical solutions of the (2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth, and can be observed in an open sea or in wide channels. The solutions are obtained by using the invariance property of the similarity transformations method <em>via</em> one-parameter Lie group theory. The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs. Under adequate restrictions, the reduced system of ODEs is solved. Numerical simulation is performed to describe the solutions in a physically meaningful way. The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein. In each animation, a frame for dominated behavior is captured. They exhibit elastic multisolitons, single soliton, doubly solitons, stationary, kink and parabolic nature. The results are significant since these have confirmed some of the established results of S. Kumar et al. (2020) and K. Sharma et al. (2020). Some of their solutions can be deduced from the results derived in this work. Other results in the existing literature are different from those in this work.</p></div>\",\"PeriodicalId\":48514,\"journal\":{\"name\":\"Journal of Ocean Engineering and Science\",\"volume\":\"8 2\",\"pages\":\"Pages 111-123\"},\"PeriodicalIF\":13.0000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Ocean Engineering and Science\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2468013321001388\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MARINE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Ocean Engineering and Science","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468013321001388","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MARINE","Score":null,"Total":0}
On similarity solutions to (2+1)-dispersive long-wave equations
This work is devoted to get a new family of analytical solutions of the (2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth, and can be observed in an open sea or in wide channels. The solutions are obtained by using the invariance property of the similarity transformations method via one-parameter Lie group theory. The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs. Under adequate restrictions, the reduced system of ODEs is solved. Numerical simulation is performed to describe the solutions in a physically meaningful way. The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein. In each animation, a frame for dominated behavior is captured. They exhibit elastic multisolitons, single soliton, doubly solitons, stationary, kink and parabolic nature. The results are significant since these have confirmed some of the established results of S. Kumar et al. (2020) and K. Sharma et al. (2020). Some of their solutions can be deduced from the results derived in this work. Other results in the existing literature are different from those in this work.
期刊介绍:
The Journal of Ocean Engineering and Science (JOES) serves as a platform for disseminating original research and advancements in the realm of ocean engineering and science.
JOES encourages the submission of papers covering various aspects of ocean engineering and science.