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

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.

Keywords

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