Symbolic computation in non-linear evolution equation: application to (3 + 1)-dimensional Kadomtsev–Petviashvili equation

The tanh method is used to find travelling wave solutions to various wave equations. In this paper, the extended tanh function method is further improved by generalizing the Riccati equation and picking up its new solutions. In order to test the validity of this approach, the (3 + 1)-dimensional Kadomtsev–Petviashvili equation is considered. As a result, the abundant new non-travelling wave solutions are obtained.