Separation of Variables and Exact Solutions of Generalized Nonlinear Klein-Gordon Equations.

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  • Changzheng Qu
    Department of Mathematics, Northwest University, Xi'an, 710069, P. R. China
  • Wenli He
    Institute of Modern Physics, Northwest University, Xi'an, 710069, P. R. China
  • Jihong Dou
    Department of Mathematics, Northwest University, Xi'an, 710069, P. R. China

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In this paper, the generalized conditional symmetry approach is developed to study the separation of variables for generalized nonlinear Klein-Gordon equations. We derive a complete list of canonical forms for a generalized nonlinear Klein-Gordon equation and a system of generalized nonlinear Klein-Gordon equations that submit to separation of variables in some coordinates. As a result, some exact solutions to the Bullough-Dodd equation, Liouville equation, Sine-Gordon equation and Sinh-Gordon equation are obtained. A symmetry group interpretation of the known results concerning separation of variables with the scalar Klein-Gordon equation is also given.

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