The extended Fan sub-equation method and its applications for a class of nonlinear evolution equations

The extended Fan sub-equation method with a computerized symbolic is used to construct the exact travelling wave solutions for a class of nonlinear evolution equations in mathematical physics. The key idea of this method is to take full advantage of general elliptic equations involving five parameters which have more new solutions and whose degeneracies can lead to special sub equation involving three parameters like Riccati equation, first kind elliptic equation, auxiliary ordinary equation, and generalized Riccati equation. As a result, many exact travelling wave solutions are obtained which include a more general soliton solutions, triangular solutions and double periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.