An improved algebra method and its applications in nonlinear wave equations

In this paper, other types of exact solution of a first-order nonlinear ordinary differential equation, which is including the algebraic method, is further investigated. By using the solutions of this equation, we give some types of solutions of the coupled KdV equation, nonlinear dispersion mK(m,n,k) equation, the variant shallow water wave equation, nonlinear dissipative equation and the higher-order nonlinear Schrodinger equation. These solutions includes compacton solutions, solitary pattern solutions, solitary wave solutions, Weierstrass elliptic function solutions, which may be useful to explain some phenomena.