# Wave amplification in the framework of forced nonlinear Schrödinger equation: The rogue wave context

@article{Slunyaev2014WaveAI, title={Wave amplification in the framework of forced nonlinear Schr{\"o}dinger equation: The rogue wave context}, author={Alexey Slunyaev and Anna Sergeeva and Efim N. Pelinovsky}, journal={Physica D: Nonlinear Phenomena}, year={2014}, volume={303}, pages={18-27} }

## 40 Citations

### Exciting extreme events in the damped and AC-driven NLS equation through plane-wave initial conditions.

- MathematicsChaos
- 2021

The wave number of a plane-wave initial condition dictates the number of emerged Peregrine-type rogue waves at the early stages of modulation instability, which is explained in terms of the global attractor possessed by the system and the asymptotic orbital stability of spatially uniform continuous wave solutions.

### The Effect of Random Wind Forcing in the Nonlinear Schrödinger Equation

- PhysicsFluids
- 2019

The influence of a strong and gusty wind field on ocean waves is investigated. How the random wind affects solitary waves is analyzed in order to obtain insights about wave generation by randomly…

### Generation of Wave Groups by Shear Layer Instability

- PhysicsFluids
- 2019

The linear stability theory of wind-wave generation is revisited with an emphasis on the generation of wave groups. The outcome is the fundamental requirement that the group move with a real-valued…

### Nonlinear stage of Benjamin-Feir instability in forced/damped deep-water waves

- Environmental Science
- 2017

We study a three-wave truncation of a recently proposed damped/forced high-order nonlinear Schrodinger equation for deep-water gravity waves under the effect of wind and viscosity. The evolution of…

### A mechanism to control and detect rogue waves by plane wave initial conditions: the prototypical example of the damped and periodically driven NLS equation

- Mathematics
- 2020

Investigating by direct numerical simulations the dynamics of the damped and forced nonlinear Schrodinger equation in the presence of a time periodic forcing and for certain parametric regimes, we…

### Transformation of envelope solitons on a bottom step

- Physics
- 2021

The transformation of surface envelope solitons travelling over a bottom step in water of a finite depth is studied. Using the transformation coefficients earlier derived in the linear approximation,…

### Analysis of the Nonlinear Spectrum of Intense Sea Wave with the Purpose of Extreme Wave Prediction

- MathematicsRadiophysics and Quantum Electronics
- 2018

We propose a method for the analysis of groups of unidirectional waves on the surface of deep water, which is based on spectral data of the scattering problem in the approximation of a nonlinear…

### Analysis of the Nonlinear Spectrum of Intense Sea Wave with the Purpose of Extreme Wave Prediction

- Mathematics
- 2018

We propose a method for the analysis of groups of unidirectional waves on the surface of deep water, which is based on spectral data of the scattering problem in the approximation of a nonlinear…

### The dynamics of surface wave propagation based on the Benjamin Bona Mahony equation

- PhysicsHeliyon
- 2020

### Bound-state soliton gas as a limit of adiabatically growing integrable turbulence

- PhysicsChaos, Solitons & Fractals
- 2023

## References

SHOWING 1-10 OF 60 REFERENCES

### Nonlinear dynamics of trapped waves on jet currents and rogue waves.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

Robustness of the long-lived analytical solutions describing modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations, suggesting a potentially higher probability of rogue waves.

### Simulations and experiments of short intense envelope solitons of surface water waves

- Physics
- 2013

The problem of existence of stable nonlinear groups of gravity waves in deep water is considered by means of laboratory and numerical simulations with the focus on strongly nonlinear waves. Wave…

### Water waves, nonlinear Schrödinger equations and their solutions

- PhysicsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- 1983

Abstract Equations governing modulations of weakly nonlinear water waves are described. The modulations are coupled with wave-induced mean flows except in the case of water deeper than the modulation…

### Energy Input Amplifies Nonlinear Dynamics of Deep Water Wave Groups

- Physics
- 2011

A possible physical mechanism for the formation of freak waves on the open ocean is the localized interactions between wind and waves. Such interactions are highly complex and are currently poorly…

### Nonlinear Wave Statistics in a Focal Zone

- Physics
- 2009

Abstract In this paper, the combined effects of refraction and nonlinearity on the evolution of ocean surface wave statistics are considered and possible implications for the likelihood of extreme…

### On nonlinear water waves under a light wind and Landau type equations near the stability threshold

- Physics
- 1980

### "Fast" nonlinear evolution in wave turbulence.

- PhysicsPhysical review letters
- 2009

It is shown by direct numerical simulation that after a strong perturbation the wave field evolves on the much faster O(epsilon;{-2}) "dynamic" time scale; here epsilon is the characteristic wave steepness.

### Nonlinear Four-Wave Interactions and Freak Waves

- Physics
- 2003

Four-wave interactions are shown to play an important role in the evolution of the spectrum of surface gravity waves. This fact follows from direct simulations of an ensemble of ocean waves using the…

### Hydrodynamic supercontinuum.

- PhysicsPhysical review letters
- 2013

Experimental observation of multi-bound-soliton solutions of the nonlinear Schrödinger equation (NLS) in the context of hydrodynamic surface gravity waves and the universal role that higher-order nonlinear perturbations to the NLS play in supercontinuum generation are reported.