The Integrability And Explicit Solutions For Several Nonlinear Equations

With the development of science and technology, nonlinear equations have becomeone of the most hot research field, which arises extensive research and applications inscience, therefore studying their integrability and analytical solutions has very impor-tant practical influence.This paper focus on three kinds of nonlinear equations: the classical Boussi-nesq equation, the variable coefcient variant-Boussinesq equation and the (2+1)-dimensional variable coefcient Broer-Kaup equation. The classical Boussinesq equa-tion is also called Broer-Kaup equation. These equations can be seen as a same typeof equation varies from constant equation to variable coefcient variant equation andlow dimensional equation to high dimensional equation. The main results as follows:the rational solutions and rogue wave solutions of the classical Boussinesq equation areobtained by using Wronskian technique; the soliton solutions and rogue wave solutionsof the variable coefcient variant-Boussinesq equation are obtained and the equation’sintegrability is also discussed with transform method; using the same method, we gotthe dromion solutions and rogue wave solutions of the (2+1)-dimensional variable co-efcient Broer-Kaup equation and discussed the equation’s integrability.