Precise solution and chaos analysis of a higher-order nonlinear Schrödinger equation in the critical point of surface gravity wave mechanics

Abstract

In this paper, we study the higher-order nonlinear Schrödinger equation of surface gravity wave evolution at the critical point \(kh\approx 1.363\). We use dynamic systems to analyse the types of solutions to this equation. Nineteen analytic chirped solutions are obtained by using the chirped wave transformation and polynomial complete discriminant system method. Finally, we add different disturbance terms to the equation and observe chaotic behaviour in the system. These results show that under different parameter conditions the frequency of the surface gravity wave changes as the amplitude changes. Therefore, the chirp \(\delta \omega \) shows a variant of patterns such as singular and periodic structures.