Solving Nonlinear Evolution Equations By Extended Three-wave Approach And Homoclinic Test Technique

This paper mainly focuses on the issues of finding exact solutions for nonlinear evolution equations, the research and discussion focus on obtaining the solitary wave solutions of nonlinear evolution equations by using expand three-wave approach and homoclinic test technique. Applying expand the three-wave approach and homoclinic test technique to the (2+1)-dimensional extension of Sine-Gordon equation and the2+1dimensional BKP equation, we obtain a typical double-wave solution, three-wave solution with the dynamic characteristics solitary solution. This has a positive significance for the discovery of a new solitary wave solutions and solitary structure. Also found that the interaction of solitary wave solutions for the (2+1)-dimensional extension of Sine-Gordon equation, including:fully elastic collision, the non-completely elastic collision and fusion. These results will help us study the interaction between high-dimensional nonlinear solitary waves.