Qualitative Analysis For Generalized Telegraph Equation And Sine-Gordon Equation

The telegraph equation is first deduced when people studied the changing law between the voltage and current in the telegraph wire. It denotes the relation between the voltage and current in equal transport wire, so it's also named the transport wire equation. The Sine-Gordon equation is a nonlinear form associated to the telegraph equation. It originates in the name of the Klein-Gordon equation in relativistic field theories. The equation was known in the 19th century and it grew greatly in importance when it was realized that it led to solutions with the collisional properties of solitons. The Sine-Gordon equation also appears in a number of the physical applications.This thesis, which is divided into two parts, is concerned with the almost periodic solutions for two common classes of the generalized Sine-Gordon and telegraph equations. And the author also gets existence and uniqueness of the solution in a certain bound.In the exordium, the author simply introduces the history and development of the almost periodic function and the equations researched. And then naturally brings up the problems investigated on.In the chapter 1, the author mainly studies the almost periodic solutionfor a class of the generalized Sine-Gordon equations. Section 1 introduces some relating definitions, prepared knowledge and symbols. And the fixed point theorem is also given. In the section 2, the author gives the definition of weak solution and maximum principle . The author then extend the results of Mawhin and Ortega's recent research.. The almost periodic solution of the generalized Sine-Gordon...