Analysis Of Solitary Wave And Chaos In Several Shallow Wave Equation

In this thesis,we study the stability of the solitary wave solutions of several shallow water wave equations and the phenomena caused by external perturbation are studied by using nonlinear dynamics theory.The chaos control problem of perturbed nonlinear dynamical systems is investigated by Melnikov method.Above all,this paper study the influence of external periodic perturbation on solitary waves of the mKdV equation.The improved Melnikov method is used to study the condition of solitary wave being transformed into chaotic state under arbitrary periodic perturbation.In addition,more disturbance frequency,the faster the speed of most purpose and numerical greater intensity of nonlinear parameter also need greater control over intensity to suppress chaos.Then,we study the existence and stability of solitary waves in the generalized Camassa-Holm equation is considered.The nonlinear intensity has important influence on the shape and stability of solitary waves.When the power of nonlinear term is odd,the equation admits positive solitary waves which are also proved to be orbitally stable when the wave velocity exceeds a critical value.When the power of nonlinear term is even,the equation admits positive and negative solitary waves which are proved to orbitally stable for any wave velocity.Finally,Using the Menikov method,all solitary waves turn to chaos under the external periodic perturbation with arbitrary nonlinear intensity.By applying a feedback controller,chaos can be controlled into a stable state.