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

Zayed, E. M. E.; Abdel Rahman, H. M.

Commun. Appl. Nonlinear Anal. 18, No. 3, 53-70 (2011).

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

Keywords:

homotopy analysis method; nonlinear evolution equations; exact solutions