%0 Journal Article
%T Variational Principles for Two Compound Nonlinear Equations with Variable Coefficients
%J Journal of Applied and Computational Mechanics
%I Shahid Chamran University of Ahvaz
%Z 2383-4536
%A Cao, Xiao-Qun
%A Peng, Ke-Cheng
%A Liu, Meng-Zhu
%A Zhang, Cheng-Zhuo
%A Guo, Ya-Nan
%D 2021
%\ 04/01/2021
%V 7
%N 2
%P 415-421
%! Variational Principles for Two Compound Nonlinear Equations with Variable Coefficients
%K Variational principle
%K calculus of variations
%K compound KdV-Burgers equation
%K Compound Burgers-BBM equation
%R 10.22055/jacm.2020.34863.2490
%X 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.
%U https://jacm.scu.ac.ir/article_15918_61efe040d838f92e3c74d13572af923c.pdf