Baecklund Transformation and Exact Solution to Kadomtsev-Petviashvili Equation with Variable Coefficients

By using homogeneous balance principle,we derive a Baecklund trans-formation(BT) to (3 1)-dimensional Kadomtsev-Petviashvili( K-P) equation with variable coefficients if the variable coefficients are linearly dependent.Based on the BT,the exact solution of the (3 1)-dimensional K-P equation is given.By the same method,we derive a BT and the solution to (2 1)-dimensional K-P equation,The variable coefficients can change the amplitude of solitary wave,but cannot change the form of solitary wave.