Variational Principles for Two Compound Nonlinear Equations ‎with Variable Coefficients

Document Type : Research Paper


1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China

2 College of Computer, National University of Defense Technology, Changsha 410073, China


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.


Main Subjects

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