A function transformation method and exact solutions to a generalized sinh-Gordon equation

Abstract

Based on a transformed Painlevé property and the variable separated ODE method, a function transformation method is proposed to search exact solutions to some partial differential equations (PDEs) with hyperbolic or exponential functions. The new approach provides a more systematical and convenient handling of the solution process for the nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painlevé property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we look for solutions to the resulting equations by some methods. As an application, exact solutions for a generalized sinh-Gordon equation are formally derived.