Using Symbolic Computation to Exactly Solve the Integrable Broer–Kaup Equations in (2+1)-Dimensional Spaces

The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.