Exact solutions for a new class of nonlinear evolution equations with nonlinear term of any order

In this paper, we consider a new class of nonlinear partial differential equations with nonlinear term of any order, utt+a1uxx+a2u+a3up+a4u2p−1=0, which contains some particular important equations. We give a new kind of transformation and a new generalized ansätze to treat this class of equations. As a result, many explicit exact solutions, which contain new kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions and combined formal solitary-wave solutions, are obtained by the extended method. In addition, we also can derive rational solutions for this class of equations.