Extended mixing exponential method and its applications

Mixing exponential method proposed by Hereman for finding the solitary wave solutions to a nonlinear evolution equation is developed and perfected. Correspondingly, an extended mixing exponential method is obtained by expressing the solutions as an infinite series of the real or complex exponential solutions of the underlying linear equations. The effectiveness of the extended approach is demonstrated by application to the well-known regular long wave equation with physical interest. Not only are steady solitary wave solutions recovered, but also the diverging and the periodic solutions are obtained.