A mapping method for obtaining exact travelling wave solutions to nonlinear evolution equations

A mapping method is described for obtaining exact travelling wave solutions to nonlinear evolution equations. By means of this method, solitary wave, periodic wave, and kink wave (or shock wave) solutions, which; are the three types of travelling waves of particular interest, can, if they exist, be obtained simultaneously for the equation in questions as long as odd- and even-order derivative terms do not coexist in the equation. A generalized Kawahara equation and sinh-Poisson equation are studied to illustrate this method, and some new results are presented.