Exact solutions for a class of nonlinear evolution equations: A unified ansätze approach

In this paper, we propose a modified generalized transformation for constructing analytic solutions to nonlinear differential equations. This improved unified ansätze is utilized to acquire exact solutions that are general solutions of simpler equations that are either integrable or possess special solutions. The ansätze is constructed via the choice of an integrable differential operator or a basis set of functions. The technique is implemented to obtain several families of exact solutions for a class of nonlinear evolution equations with nonlinear term of any order. In particular, the Klein–Gordon, the Sine–Gordon and Landau–Ginburg–Higgs equations are chosen as examples to illustrate the method.