• Title of article

    Variational Principles for Two Compound Nonlinear Equations with Variable Coefficients

  • 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

  • Pages
    7
  • From page
    415
  • To page
    421
  • 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
  • Journal title
    Journal of Applied and Computational Mechanics
  • Serial Year
    2021
  • Record number

    2558235