Author/Authors :
Cao, Xiao-Qun College of Meteorology and Oceanography - National University of Defense Technology, Changsha, China , Peng, Ke-Cheng College of Meteorology and Oceanography - National University of Defense Technology, Changsha, China , Liu, Meng-Zhu College of Meteorology and Oceanography - National University of Defense Technology, Changsha, China , Zhang, Cheng-Zhuo College of Meteorology and Oceanography - National University of Defense Technology, Changsha, China , Guo, Ya-Nan College of Meteorology and Oceanography - National University of Defense Technology, Changsha, China
Abstract :
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 trialLagrange 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.
Keywords :
Variational principle , Calculus of variations , Compound KdV-Burgers equation , Compound Burgers-BBM equation
