The tanh method: I. Exact solutions of nonlinear evolution and wave equations

Abstract

A systemized version of the tanh method is used to solve particular evolution and wave equations. If one deals with conservative systems, one seeks travelling wave solutions in the form of a finite series in tanh. If present, boundary conditions are implemented in this expansion. The associated velocity can then be determined a priori, provided the solution vanishes at infinity. Hence, exact closed form solutions can be obtained easily in various cases.