A powerful approach to study the new modified coupled Korteweg–de Vries system

Abstract

In this work, the q-homotopy analysis transform method (shortly q-HATM) which is a combined form of q-homotopy analysis method and Laplace transform method is employed to find numerical solution to the new modified coupled Korteweg–de Vries system. This method allows us to fine-tune the convergence region along with rate of convergence of the obtained series solution by allowing the auxiliary parameters n and ħ to vary. The obtained solution by the proposed method is presented in a refined convergent series form. The numerical results show that only few terms are sufficient to obtain an approximate solution which is accurate, efficient, and reliable. Furthermore, the graphical depictions of the obtained approximate solution of the system are presented.