Abstract
A nonlinear transformation to a generalized KP equation with general variable coefficients (gvcKP) has been derived by using the simplified homogeneous balance method (SHB). The nonlinear transformation converts gvcKP into a quadratic homogeneity equation to be solved. The quadratic homogeneity equation admits exponential function solutions, thus one-soliton and two-soliton solutions of gvcKP can be obtained by means of the nonlinear transformation derived in the paper. As the special cases of gvcKP, several generalized KP equations with different form and the corresponding results of them are also given.
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