The homotopy analysis method for solving the nonlinear evolution equations in mathematical physics.(English)Zbl 1236.35161

Summary: By means of the homotopy analysis method (HAM) the exact solutions of the $$(1+1)$$-dimensional nonlinear combined KdV-MKdV equation and the $$(1+1)$$-dimensional Jaulent-Miodek (JM) equations are exactly obtained. HAM is a powerful and easy to use the analytic tool for the nonlinear evolution equations. The validity of this method is proven successful by applying it to these nonlinear equations.

MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 65L99 Numerical methods for ordinary differential equations 47J35 Nonlinear evolution equations