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Nearly integrable turbulence and rogue waves in disordered nonlinear Schrödinger systems
Zhi-Yuan Sun1,2, Xin Yu1
1Institute of Fluid Mechanics, Beihang University, Beijing 100191, China.
Physical Review. E
|July 17, 2021
Summary
Adding weak system noise to nonlinear Schrödinger (NLS) equations significantly increases the probability of extreme rogue wave (RW) events. This finding enhances understanding of disorder effects in nonlinear systems.
Area of Science:
- Nonlinear dynamics
- Wave propagation
- Complex systems
Background:
- Integrable nonlinear Schrödinger (NLS) systems are crucial for studying nonlinear wave phenomena.
- Extreme events like rogue waves (RWs) are of significant scientific interest.
- The impact of inherent disorder (e.g., turbulence, random fluctuations) on these systems is not well understood.
Purpose of the Study:
- To investigate the influence of disorder on rogue wave occurrence in nearly-integrable NLS systems.
- To explore how weak system noise affects the probability of extreme nonlinear events.
- To provide a qualitative explanation for the observed phenomena.
Main Methods:
- Numerical experiments were conducted on two nearly-integrable NLS equations.
- The effect of weak system noise (disorder) was systematically introduced.
- Linear and nonlinear spectral analyses were employed to interpret the results.
Main Results:
- The addition of weak system noise was found to significantly increase the probability of rogue wave (RW) occurrence.
- The findings demonstrate a clear interplay between disorder and nonlinearity.
- Spectral analyses provided qualitative support for the observed increase in RW events.
Conclusions:
- Disorder, even at weak levels, can dramatically enhance extreme nonlinear events like rogue waves in NLS systems.
- The study offers insights into the complex dynamics of nonlinear waves in the presence of noise.
- Results may guide future experimental research in fluid dynamics, optics, and quantum condensates.
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