A Class Of Generalized Mkdv Side Traveling Wave Solutions To The Branch

By using the theory of bifurcations of dynamical systems to the generalization form of the modified KdV equation, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. At the same time , the paper study a coupled nonlinear wave equations, the existence and stability of periodic wave solutions by Hopf bifurcations are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence and stability of the above solutions are given.In chapter 1, the paper introduce the bifurcations for traveling wave solutions for the generalization form of the modified KdV equation. In section 1.1 the paper introduce the corresponding model and results. In section 1.2 we discuss bifurcations of phase portraits (1.1.4). In section 1.3, we consider the existence of smooth solitary, kink traveling wave and periodic traveling wave solutions of (1.1.1). In section 1.4, we show the existence of breaking solutions uncountably infinite many non-smooth periodic traveling wave solutions of (1.1.1).In chapter 2, the paper introduce bifurcations of traveling wave solutions for the coupled nonlinear wave equations. In section 2.1, we introduce the corresponding model and results. In section 2.2, we study the Hopf bifurcations of (2.2.5) as some parametric given.