• P-ISSN 0974-6846 E-ISSN 0974-5645 # Indian Journal of Science and Technology

## Article • VIEWS 766
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Indian Journal of Science and Technology

Year: 2020, Volume: 13, Issue: 24, Pages: 2387-2403

Original Article

## Solving the cubic complex Ginzburg-Laundau equation by Homotopy analysis method

Received Date:22 May 2014, Accepted Date:26 July 2015, Published Date:09 July 2020

## Abstract

Objectives: This paper obtains the series solution of the cubic complex Ginzburg-Laundau equation, by means of homotopy analysis method(HAM). Methods: In addition to the homotopy analysis method, homotopy perturbation and Adomian decomposition methods are applied to determine approximation solution of the cubic complex Ginzburg-Laundau equation and advantage of using HAM. Also a theorem is proved to guarantee the convergence of the HAM to solve this equation. Findings: Three examples are solved to illustrate the efficiency of the proposed method, this method is compared with other analytical approximate methods such as homotopy perturbation method (HPM)and Adomiam decomposition method(ADM) and it can be seen that these methods have the same results for this equation. Application: Homotopy analysis method as a reliable and valid scheme can be used to work out the cubic complex Ginzburg-Laundau equation which is nonlinear partial differential equation.

Keywords: Homotopy analysis method; Ginzburg-Laundau

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