New multi-hump exact solitons of a coupled Korteweg-de-Vries system with conformable derivative describing shallow water waves via RCAM

TL;DR

This paper introduces a modified approximation method to find exact multi-hump soliton solutions of a coupled KdV system with conformable derivatives, revealing new wave features in shallow water models.

Contribution

A novel modified scheme is developed to obtain exact multi-hump soliton solutions of conformable derivative KdV equations, demonstrating new wave features.

Findings

Solutions exhibit multi-hump soliton structures

Tails decay exponentially and monotonically

Method proves efficient for conformable derivative equations

Abstract

In this article, a modification of the rapidly convergent approximation method is proposed to solve a coupled Korteweg-de Vries equations with conformable derivative that govern shallow-water waves. Based on the Leibniz and chain rule of conformable derivative, these equations reduced into ODEs with integer-order using traveling wave transformation. Adopting the modified scheme a new novel exact solution of the reduced coupled ordinary differential equations is obtained in terms of exponential functions. Finally, by putting them back into traveling wave transformation the solutions of the considered partial differential equations with conformable derivative are derived. To ensure the boundedness of the derived solutions few theorems have been proposed and proved. The derived results of the theorems are utilized to plot the solutions. Graphics exhibit that solutions have variant multi-hump soliton peculiarities and their tails decay to zero exponentially in a monotonic manner. These results not only show the efficiency of the modified scheme but also establish that the solution is enriched with new multi-hump features.