An analytical method for finding exact Traveling wave solutions of some nonlinear Evolution equations (nlees) in biological and Mathematical problems

Abstract

Most of the natural happenings can be present by nonlinear modeling. The soliton theory is a highly effective section of nonlinear sciences that includes soliton, multi-soliton, rational, breather line, breather kinky, lump and rogue wave solutions. Such solutions are essential to realizing the internal properties of the nonlinear models. This dissertation presents exact traveling wave solutions of the three nonlinear models such as the (2+1) Bogoyavlenskii’s breaking soliton (BBS) equation, the (2+1)-dimensional Benjamin-Bona-Mahony-Burgers (BBMB) equation and the (3+1)-dimensional Sharma–Tasso–Olver-like (STOL) equation by applying Hirota bilinear method. By this method, we construct the bilinear form and find the interaction solutions of the above three models. We determine the multi-soliton and their interaction solutions of the BBS model and STOL model. Various properties of the obtained solutions are illustrated clearly with a number of 3D plot, 2D plot, density plot, curve plot and contour plot by choosing suitable parametric values via the computational software Maple 18.