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

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.

A rapidly convergent approximation scheme for nonlinear autonomous and non-autonomous wave-like equations

“…A few analytical methods such as method based on symmetry analysis (Lie group theoretic approach) [1,2], Hirota bilinear method [3], inverse scattering transformation method [4,5], Prelle-Singer method [6], the method involving Jacobi last multiplier [7], Tanh, Sech, Exp method [8,9], Jacobi elliptic function method [10] and so on, analytical approximation schemes such as homotopy analysis method (HAM) [11,12], Adomian decomposition method (ADM) [13], Fourier transform Adomian decomposition method (FTADM) [14], rapidly convergent approximation method (RCAM) [15][16][17][18][19][20][21][22][23] etc., numerical methods viz. finite difference/element methods [24,25], Galerkin or collocation methods are used to find the solution of mathematical models.…”