The Homotopy Analysis Method for Explicit Analytical Solutions of Jaulent–Miodek Equations

In this work, the homotopy analysis method (HAM) is applied to obtain the explicit analytical solutions for system of the Jaulent–Miodek equations. The validity of the method is verified by comparing the approximation series solutions with the exact solutions. Unlike perturbation methods, the HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniques, theHAMprovides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter
. Briefly speaking, this work verifies the validity and the potential of the HAM for the study of nonlinear systems.

homotopy analysis method; Jaulent-Miodek equation; system of nonlinear partial differential equations