Dynamics of Rogue Waves for a Generalized Inhomogeneous Third-Order Nonlinear Schrödinger Equation From the Heisenberg Ferromagnetic System

Ni Song,Hui Xue

doi:10.1109/access.2019.2926541

Abstract

In this paper, dynamics of the higher-order rogue waves for a generalized inhomogeneous third-order nonlinear Schrodinger equation is investigated by using the generalized Darboux transformation. Based on the Lax pair, the first-order to the third-order rogue wave solutions are derived through algebraic iteration starting from a seed solution. Nonlinear dynamical properties of rogue waves are analyzed on the basis of 3-D plots and density profiles. The new arrangement of the higher-order rogue waves is obtained. It is helpful to study the phenomenon of rogue waves in the Heisenberg ferromagnetic system.

Highlights

Rogue waves, originated from the ocean dynamics, are shortpeak waves with large amplitude above several tens of meters, which rise from the surrounding waves and have little relationship with the neighboring ones
In this paper, we investigated the higher-order rogue waves of a generalized inhomogeneous third-order nonlinear Schrödinger equation
Based on the classical Darboux transformation (DT), the generalized DT is deduced by using Taylor expansion and limit procedures

Summary

INTRODUCTION

Rogue waves, originated from the ocean dynamics, are shortpeak waves with large amplitude above several tens of meters, which rise from the surrounding waves and have little relationship with the neighboring ones They exist for a short time and disappear very quickly. Song et al constructed the higher-order rogue wave solutions for the inhomogeneous fourth-order nonlinear Schrödinger equation by using the generalized DT [20]. Chen et al obtained the higher-order rational solutions and rogue wave solutions for a (2+1)-dimensional nonlinear Schrödinger equation [21]. Inspired by the pioneers’ works, a generalized inhomogeneous third-order nonlinear Schrödinger equation will be discussed [26]. The generalized DT is established for an inhomogeneous third-order nonlinear Schrödinger equation. Numerical simulations are carried out and dynamical characteristics are analyzed by selecting different parameters

GENERALIZED DARBOUX TRANSFORMATION

ROGUE WAVE SOLUTIONS

FIRST-ORDER ROGUE WAVE SOLUTION

SECOND-ORDER ROGUE WAVE SOLUTION Putting more attention on the limitation

THIRD-ORDER ROGUE WAVE SOLUTION Taking the following limit into account

CONCLUSIONS