  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.
