Rational Waves and Complex Dynamics: Analytical Insights into a Generalized Nonlinear Schrödinger Equation with Distributed Coefficients

Abstract

In this paper, we first present a complex multirational exp-function ansatz for constructing explicit solitary wave solutions, N-wave solutions, and rouge wave solutions of nonlinear partial differential equations (PDEs) with complex coefficients. To illustrate the effectiveness of the complex multirational exp-function ansatz, we then consider a generalized nonlinear Schrödinger (gNLS) equation with distributed coefficients. As a result, some explicit rational exp-function solutions are obtained, including solitary wave solutions, N-wave solutions, and rouge wave solutions. Finally, we simulate some spatial structures and dynamical evolutions of the modules of the obtained solutions for more insights into these complex rational waves. It is shown that the complex multirational exp-function ansatz can be used for explicit solitary wave solutions, N-wave solutions, and rouge wave solutions of some other nonlinear PDEs with complex coefficients.

Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

“…First-order fractional rogue wave solution (33) can also obtained by using the limits lim k⟶0 v (2α) k as did in [14] and equation (28); here,…”

“…ough different from tsunami, the rogue waves that occur in the ocean have extraordinary destructiveness. Recently, rogue waves especially optical ones gained high attention [2][3][4][5][6][7][8][9][10][11][12][13][14]. It is Solli et al [2] who reported the optical rogue waves generated through a generalized NLS equation.…”

Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics

“…Semidiscrete systems keep some or all their spatial variables discrete while time continuous systems have an important role in simulating complex phenomena in many fields, for instance; they often arise in high energy physics as approximations of continuum models for the numerical simulation of nonlinear soliton dynamics [1]. It is Toda [2] who first derived the classical semidiscrete system-Toda lattice when the lattice with exponential interaction was considered. Like the famous Kortweg-de Vries equation, the classical Toda lattice is one of the most important completely integrable systems, and the multisoliton solutions of which have very important significance to the study of many nonlinear problems in atomic and particle physics.…”

“…It should be noted that system (1) is not only different from the known ones [2,[6][7][8][9][10][11][12][13][14][15][44][45][46]:…”

“…In the literature, there is no research result about semidiscrete system (1). Constructing or solving semidiscrete systems is a significant work in the theory of nonlinear lattices [2]. In 1990, Tu [48] proposed a scheme for generating hierarchies of semidiscrete integrable systems.…”