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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