A novel approach to study generalized coupled cubic Schrödinger–Korteweg-de Vries equations

• A generalized coupled cubic Schrödinger–Korteweg-de Vries equations is studied. • This coupled model simulates the interaction of long and short waves which is important in many domains of applied sciences and engineering. • The modified Sardar sub-equation is used. • New solitons and solitary wave solutions are achieved. • Some plots are presented to clearly illustrate the dynamic features of these solutions. The Kortewegde Vries (KdV) equation represents the propagation of long waves in dispersive media, whereas the cubic nonlinear Schrödinger (CNLS) equation depicts the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A model that couples these two equations seems intriguing for simulating the interaction of long and short waves, which is important in many domains of applied sciences and engineering, and such a system has been investigated in recent decades. This work uses a modified Sardar sub-equation procedure to secure the soliton-type solutions of the generalized cubic nonlinear Schrödinger–Korteweg-de Vries system of equations. For various selections of arbitrary parameters in these solutions, the dynamic properties of some acquired solutions are represented graphically and analyzed. In particular, the dynamics of the bright solitons, dark solitons, mixed bright-dark solitons, W-shaped solitons, M-shaped solitons, periodic waves, and other soliton-type solutions. Our results demonstrated that the proposed technique is highly efficient and effective for the aforementioned problems, as well as other nonlinear problems that may arise in the fields of mathematical physics and engineering.