Navigating waves: Advancing ocean dynamics through the nonlinear Schrödinger equation

Abstract

The nonlinear Schrödinger equation, held in high regard in the realms of plasma physics, fluid mechanics, and nonlinear optics, reverberates deeply within the field of ocean engineering, imparting profound insights across a plethora of phenomena. This article endeavours to establish a connection between the equation’s theoretical framework and its practical applications in ocean engineering, presenting a range of solutions tailored to grasp the intricacies of water wave propagation. By employing three methodologies, namely, the simplest equation method, the ratio technique, and the modified extended tanh-function method, we delineate various wave typologies, encompassing solitons and periodic manifestations. Enhanced by visual representations, our findings have the potential to deepen the comprehension of wave dynamics, with promising implications for the advancement of ocean engineering technologies and the refinement of marine architectural design.

Keywords

• nonlinear schrödinger equation
• multisoliton
• ocean engineering
• simplest equation method
• [1/φ(ς), φ′(ς)/φ(ς)] method
• modified extended tanh-function method
• nonlinear equations