Exact solitary wave solutions of non-linear evolution equations

Publisher Summary This chapter describes a mechanization method for solving nonlinear evolution equations exactly and systematically. The method proceeds by reducing evolution equations to polynomial equations and solving the latter using Wu's method. The method is illustrated by solving several well-known equations, including the KdV-Burgers equation, the Kawachara equation, the Burgers–Huxley equation, and a variant of Boussinesq equations. A number of other equations and their exact solitary wave solutions found by using this method are provided in the tablular form, which demonstrates the wide applicability of the method. The single solitary wave solutions for a variety of nonlinear evolution equations are discussed in this chapter. The nonlinear Schrodinger and the sine-Gordon equations are notable exceptions, though their solutions contain hyperbolic functions as well. The method is readily applicable to (2 + 1)-dimensional equations such as the K-P equation. The modification of the method to treat complex, higher-dimensional, or vector nonlinear evolution equations or PDEs of a different kind is also explained.