Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients

It is very important to seek explicit variational principles for nonlinear partial differential equations, which are theoretical bases for many methods to solve or analyze the nonlinear phenomena and problems. By designing the modified trial-Lagrange functional, different variational formulations ar...

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Main Authors:	Xiao-Qun Cao, Ke-Cheng Peng, Meng-Zhu Liu, Cheng-Zhuo Zhang, Ya-Nan Guo
Format:	Article
Language:	English
Published:	Shahid Chamran University of Ahvaz 2021-04-01
Series:	Journal of Applied and Computational Mechanics
Subjects:	variational principle calculus of variations compound kdv-burgers equation compound burgers-‎bbm equation
Online Access:	https://jacm.scu.ac.ir/article_15918_61efe040d838f92e3c74d13572af923c.pdf

id	doaj-260b10656d244bb59df154f28379c5cb
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spelling	doaj-260b10656d244bb59df154f28379c5cb2021-02-04T16:51:01ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362383-45362021-04-017241542110.22055/jacm.2020.34863.249015918Variational Principles for Two Compound Nonlinear Equations ‎with Variable CoefficientsXiao-Qun Cao0Ke-Cheng Peng1Meng-Zhu Liu2Cheng-Zhuo Zhang3Ya-Nan Guo4College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, ChinaCollege of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, ChinaCollege of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, ChinaCollege of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, ChinaCollege of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, ChinaIt is very important to seek explicit variational principles for nonlinear partial differential equations, which are theoretical bases for many methods to solve or analyze the nonlinear phenomena and problems. By designing the modified trial-Lagrange functional, different variational formulations are successfully and firstly established by the semi-inverse method for two kinds of compound nonlinear equation, i.e. the KdV-Burgers equation and the Burgers-BBM equation, respectively. Both of them contain the variable coefficients, which are time-dependent. Furthermore, the obtained variational principles are proved correct by minimizing the functionals with the calculus of variations.https://jacm.scu.ac.ir/article_15918_61efe040d838f92e3c74d13572af923c.pdfvariational principlecalculus of variationscompound kdv-burgers equationcompound burgers-‎bbm equation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xiao-Qun Cao Ke-Cheng Peng Meng-Zhu Liu Cheng-Zhuo Zhang Ya-Nan Guo
spellingShingle	Xiao-Qun Cao Ke-Cheng Peng Meng-Zhu Liu Cheng-Zhuo Zhang Ya-Nan Guo Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients Journal of Applied and Computational Mechanics variational principle calculus of variations compound kdv-burgers equation compound burgers-‎bbm equation
author_facet	Xiao-Qun Cao Ke-Cheng Peng Meng-Zhu Liu Cheng-Zhuo Zhang Ya-Nan Guo
author_sort	Xiao-Qun Cao
title	Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients
title_short	Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients
title_full	Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients
title_fullStr	Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients
title_full_unstemmed	Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients
title_sort	variational principles for two compound nonlinear equations ‎with variable coefficients
publisher	Shahid Chamran University of Ahvaz
series	Journal of Applied and Computational Mechanics
issn	2383-4536 2383-4536
publishDate	2021-04-01
description	It is very important to seek explicit variational principles for nonlinear partial differential equations, which are theoretical bases for many methods to solve or analyze the nonlinear phenomena and problems. By designing the modified trial-Lagrange functional, different variational formulations are successfully and firstly established by the semi-inverse method for two kinds of compound nonlinear equation, i.e. the KdV-Burgers equation and the Burgers-BBM equation, respectively. Both of them contain the variable coefficients, which are time-dependent. Furthermore, the obtained variational principles are proved correct by minimizing the functionals with the calculus of variations.
topic	variational principle calculus of variations compound kdv-burgers equation compound burgers-‎bbm equation
url	https://jacm.scu.ac.ir/article_15918_61efe040d838f92e3c74d13572af923c.pdf
work_keys_str_mv	AT xiaoquncao variationalprinciplesfortwocompoundnonlinearequationswithvariablecoefficients AT kechengpeng variationalprinciplesfortwocompoundnonlinearequationswithvariablecoefficients AT mengzhuliu variationalprinciplesfortwocompoundnonlinearequationswithvariablecoefficients AT chengzhuozhang variationalprinciplesfortwocompoundnonlinearequationswithvariablecoefficients AT yananguo variationalprinciplesfortwocompoundnonlinearequationswithvariablecoefficients
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Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients

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