English abstract
In this project, we investigate exact solutions of certain nonlinear evolution equation of dispersive and dissipative nature by using different methods such as hyperbolic method, series method and jacobi elliptic function method
In chapter (1), we derive Non-dimensional shallow water equations by using equation of continuity, equation of inotion and boundary conditions for surface water wave problem. Then shallow water equations have been used to derive korteweg de Vries (KdV) equation and we use Jacobian elliptic functions to get solitary waves solution of KdV equation. In chapter (2), we deal with different examples of nonlinear evolution and wave equation and we solve it with the aid of tanh method. We use Maple7 programming to solve some equations and to draw the graph of solutions. In chapter (3), we use series method to derive the solitary wave solution for a modified KdV equation, the kink wave solution for a combined KdV-mKDV equation and we do phase plane analysis of a coupled wave equation which gives justification for choosing the special value a parameter in the series method. Finally, in chapter (4) we used mapping method and modified mapping method to derive the Jacobian elliptic function solutions for the combined KdV-mKDV equation and the squared Jacobian elliptic function solutions for the (2+1)-dimensional Kadomtsev Petviashvili equation and we draw the graphs for some solutions.
