Solving the coupled Schrödinger -Korteweg- de-Vries system by modified variational iteration method with genetic algorithm

Ali Mustafa; Waleed Al-Hayani

doi:10.31185/wjcm.127

Solving the coupled Schrödinger -Korteweg- de-Vries system by modified variational iteration method with genetic algorithm

Authors

Ali Mustafa University of Mosul/College of Computer Science and Mathematics
Waleed Al-Hayani Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Iraq

DOI:

https://doi.org/10.31185/wjcm.127

Keywords:

coupled Schrödinger–KdV equation, Genetic Algorithm, Lagrange multiplier, Variational iteration method, Modified variational iteration method

Abstract

A system of nonlinear partial differential equations was solved using a modified variational iteration method (MVIM) combined with a genetic algorithm. The modified method introduced an auxiliary parameter (p) in the correction functional to ensure convergence and improve the outcomes. Before applying the modification, the traditional variational iteration method (VIM) was used firstly. The method was applied to numerically solve the system of Schrödinger-KdV equations. By comparing the two methods in addition to some of the previous approaches, it turns out the new algorithm converges quickly, generates accurate solutions and shows improved accuracy. Additionally, the method can be easily applied to various linear and nonlinear differential equations.

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