భౌతిక గణితం

Construction of Super NLPDE’s Traveling Waves Solutions of Super KdV Equation with Emphasis to Applications

Abstract

HI Abdel-Gawad

Construction of super NLPDE’s is performed to the aim of finding novel dynamic evolution equations that describe highly dispersive nonlinear systems. It is found that a coupled NLPDE generates a super NLPDE. Which may reveal novel nonlinear phenomena and provide an interpretation of the phenomena complexity. Attention is focused to find the super formulation of the nonlinear, coupled nonlinear Schrodinger (NLS, CNLS), Davey-Stwartson (generalized Zakharov), Higg’s, and coupled KdV equations. The CNLS equation may help to control the propagation of soliton (pulse) waves in fiber optics. These equations are currently used in engineering such as the management of the concept of soliton in the development of modern technology via the study of Bose-Einstein condensate phenomena. Further, to test the behavior and study the characteristics of the propagation of laser pulse and high-power fiber laser applications. Here, the extended unified method is used to find the solutions of the traveling wave to the super KdV equation. These solutions show solitary, soliton with double kinks waves and lumps. We think that the novel equations constructed here will open a new trend of research that may lead new phenomena in the applied sciences.