Research On The Traveling Wave Solutions For Two Classes Of Nonlinear Wave Equations

In recent years, with the purpose of application, the study of nonlinear wave equations which reflect the problems of physics, optics and other disciplines has become a focus of scholars in various fields. How to solve the nonlinear wave equation has become an important part of nonlinear problems for a lot of research scientists above, which has very important theoretical value and practical significance. So far, the method of nonlinear wave equations has been developed to a dozen. such as Fan sub-equation method, Lie group method, Darboux transformation method, sine-cosine method, extended tanh method homogenous balance method, bifurcation theory method of dynamic systems and so on. These methods have obtained a lot of new solitary wave solutions, which greatly promote the development of the theory of nonlinear science.In the paper, from the physical to the practical problems of general (2+1)-dimensional breaking soliton equation and coupled Higgs field equation are acted as the study. with the use of sine-cosine method and extended tanh method, the general (2+1)-dimensional breaking soliton equation is investigated, after applying Maple mathematical software to numerical calculation and simulation, a lot of explicit and exact traveling wave solutions which including solitary wave solutions, periodic wave solutions and compact solutions are get in the different parametric conditions; At the same time by using the bifurcation method of dynamic systems to discuss the branch situation of traveling wave solutions of the coupled Higgs field equation, sufficient conditions to guarantee the existence of new solitary wave solutions and the uncountable infinite number of periodic wave solutions are given. And all exact explicit parametric representations of the above wave solutions are determined.