The Soliton Solutions Of A Nonlinear Dispersive Equation

In this paper, in order to look for the new soliton solutions, we introduce a new nonlinear shallow water wave equation. In the third chapter, the qualitative analysis methods of dynamical system are used to investigate the peaked wave solutions of the osmosis k(2,2) equation. Using the way of the phase portrait bifurcation analysis and mathematical software, we obtain the explicit expression of peaked wave solutions by the solutions corresponding to the homoclinic orbit and the periodic orbit. In the forth chapter, the k(2,2) equation with parameter dispersion ,which is a more complicated and completed system equation, is investigated, and the explicit expression of peaked wave solutions and the simulated image are given. In the fifth chapter, the extended DP equation with parameter dispersion is studied, the soliton solutions are obtained.