Analytical study of rational and double-soliton rational solutions governed by the KdV–Sawada–Kotera–Ramani equation with variable coefficients

In this work, we construct rational and double-soliton rational solutions of the KdV–Sawada–Kotera–Ramani equation with variable coefficients by using the unified method and its generalized form. We employ these methods to obtain soliton rational solutions, periodic rational solutions, elliptic rational solutions, and two-soliton rational solutions. Here, we study the nonlinear interactions between these solutions and the collision between the long surface water waves. Also, we discuss the dynamical behavior of the traveling wave solutions and their structures.