Mathematical analysis of the Generalized Benjamin and Burger-Kdv Equations via the Extended Trial Equation Method

Abstract

In this paper, using the Extended Trial Equation (ETEM), we get new traveling wave solutions of the Generalized Benjamin, the Generalized Burger-Kdv Equations (GBE, GBKE). The obtained solutions not only constitute a novel analytical viewpoint in nonlinear complex phenomena, but they also form a new stand alone basis from which physical applications in this arena can be comprehended further, and moreover investigated. Furthermore, to concretely enrich this research production, we provide illustrative, Mathematica Release 7 based, 3D graphics of the gotten solutions, with well chosen, yet structure revealing parameters.