### Solving Coupled Hirota System by Using Homotopy Perturbation and Homotopy Analysis Methods

Rostam K. Saeed1 and Rebwar S. Muhammad1

1Salahaddin University, College of Science - Department of Mathematics, Kurdistan Region, Erbil-Iraq,

Abstract
In this paper, two methods, namely Homotopy Perturbation Method
(
HPM) and Homotopy Analysis Method (HAM) are applied to obtain approximate
solutions of the nonlinear coupled Hirota system (
CHS). We see that these two
methods are efficient and effectives for solving nonlinear CHS and the obtained
results of the two methods coincide with each other. In our work, Maple 13 has
been used for computations.

Key Words: Homotopy Perturbation Method, Homotopy Analysis Method, Coupled Hirota System, analytical solution.

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