Construction Of Exact Travelling And Solitary Wave Solutions For Some Nonlinear PDEs

The nonlinear partial differential equations have marvelous applications in the field of science and engineering.It is a great importance to study the exact traveling and solitary wave solutions for nonlinear wave models to understand the nature of nonlinear problems and explain the different scientific nonlinear phenomena.Therefore,to finding the exact traveling and solitary wave solutions for nonlinear models have always been an great deals of interest to large group of scientist,engineer,physicists and mathematician in the field of nonlinear science.In this study,we used the four different types of techniques to construct the exact traveling and solitary wave solutions of some important nonlinear PDEs.The extension of auxiliary equation mapping method used for the construction of solitary wave solutions for modified Korteweg-de Vries and further modified Korteweg-de Vries equations.Extension of direct algebraic mapping method applied for the construction of exact traveling and solitary wave solutions for longitudinal wave equation in a magneto-electro-elastic circular rod and system of dynamical equations for the ion sound and Langmuir waves.For the constructions of exact traveling and solitary wave solutions for(2+1)-dimensional Zakharov-Kuznetsov equation,generalized(2+1)-dimensional Zakharov-Kuznetsov equation,generalized form of modified(2+1)-dimensional Zakharov-Kuznetsov equation,Whitham-Broer-Kaup equation,the(2+1)-dimensional Broer-Kaup-Kupershmit equation,Drinfel'd-Sokolow-Wilson equation,generalized Zakharov-Kuznetsov modified equal width equation by applied the modification of extended auxiliary equation mapping method.The extension of modified rational expansion method applied on the(2+1)-dimensional nonlinear Nizhnik-NovikovVesselov equation for constructing the exact traveling and solitary wave solutions.These models studied in this thesis have a good application background in the field of modern science.We have obtained the bright-dark solitons,singular-combined solitons,kink wave and anti-kink wave solitons,periodic solitary wave,traveling wave,dispersive solitary wave solutions of very complex nonlinear models,which did not be find in the past literature.In this study,we also show some obtained solutions with two and three dimensional graphically with the help of symbolic computation.The obtained results prove that the techniques which apply in this research work are powerful and effective for finding the exact traveling and solitary wave solutions of various nonlinear complex models in Mathematical physics,engineering and different branches of physical sciences.