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Updated: Aug 27, 2025
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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Dynamics study of integrable turbulence with fourth-order nonlinear Schrödinger equation
Yaning Tang1, Yan Wang1, Dingwei Wu2
1School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, People's Republic of China.
Chaos (Woodbury, N.Y.)
|October 1, 2022
Summary
Control parameters influence rogue wave (RW) generation in optical and spin systems. Collisions between solitons and breathers are key mechanisms for RW formation in turbulent states.
Area of Science:
- Applies to nonlinear optics and condensed matter physics, specifically Heisenberg spin systems.
- Focuses on the fourth-order nonlinear Schrödinger equation (NLSE).
Background:
- The fourth-order NLSE models phenomena in optical and Heisenberg spin systems.
- Investigates continuous waves perturbed by one-dimensional random rough surfaces as initial conditions.
Purpose of the Study:
- To numerically resolve eigenvalues and simulate the evolution of the fourth-order NLSE.
- To understand the formation mechanisms of rogue waves (RWs) in integrable turbulence.
- To analyze the influence of control parameters on RW generation and soliton dynamics.
Main Methods:
- Employs the Fourier collocation method for eigenvalue resolution.
- Utilizes the symmetrical split-step Fourier method for simulating wave evolution.
- Analyzes a large number of initial conditions to investigate steady chaotic states.
Main Results:
- Control parameters significantly affect the number and intensity of rogue waves (RWs).
- Identified an inflection point where control parameters influence soliton velocities and RW generation.
- Confirmed that collisions between breathers and solitons generate RWs.
Conclusions:
- The study provides insights into the turbulent state of the system.
- Elucidates the formation mechanisms of rogue waves.
- Highlights the critical role of control parameters and soliton interactions in RW genesis.
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