Complexiton solutions for complex KdV equation by optimal Homotopy Asymptotic Method

Abstract

In this article an innovative technique named as Optimal Homotopy Asymptotic Method has been explored to treat system of KdV equations computed from complex KdV equation. By developing special form of initial value problems to complex KdV equation, three different types of semi analytic complextion solutions fromcomplexKdVequation have been achieved. First semi analytic position solution received fromtrigonometric form of initial value problem, second is semi analytic negation solution received by hyperbolic form of initial value problem and third one is special type of semi analytic solution expressed by the combination of trigonometric and hyperbolic functions. It was proved that only first order OHAM solution is accurate to the closed-form solution.