Auto-Bäcklund transformation and new exact solutions of the (3+1)-dimensional KP equation with variable coefficients

The (3+1)-dimensional variable coefficient Kadomtsev-Petviashvilli equation describes the dynamics of solitons andnonlinear waves in plasmas and superfluids. Based on computerized symbolic computation and extended variablecoefficient homogeneous balance method, several families of exact soliton-like solutions, rational solutions, and auto-Bäcklund transformation are presented. With the use of the auto-BT and the ε-expansion method, we can obtain asoliton-like solution including N-solitary wave of the (3+1)-dimensional Kadomtsev-Petviashvilli equation with variablecoefficients. Especially, we get a soliton-like solution including two-solitary waves as an illustrative example in detail.

کلیدواژه ها:

Symbolic computation ، ε-expansion method ، Plasmas ، Auto-Bäcklund transformation ، Two-solitary waves