Exact Solutions to a Combined sinh-cosh-Gordon Equation |
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Authors: | WEI Long |
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Affiliation: | Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China |
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Abstract: | Based on a transformed Painlevé property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of 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 seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived. |
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Keywords: | function transformation method variable separated ODE method combined sinh-cosh-Gordon equation |
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