# Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

## Abstract

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.

- Authors:

- Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22472252

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Experimental and Theoretical Physics

- Additional Journal Information:
- Journal Volume: 120; Journal Issue: 5; Other Information: Copyright (c) 2015 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7761

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; LAGRANGIAN FUNCTION; NONLINEAR PROBLEMS; QUADRATURES; RANDOMNESS; SCHROEDINGER EQUATION; SURFACES; VARIATIONAL METHODS; WAVE PACKETS

### Citation Formats

```
Ruban, V. P., E-mail: ruban@itp.ac.ru.
```*Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation*. United States: N. p., 2015.
Web. doi:10.1134/S1063776115050179.

```
Ruban, V. P., E-mail: ruban@itp.ac.ru.
```*Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation*. United States. doi:10.1134/S1063776115050179.

```
Ruban, V. P., E-mail: ruban@itp.ac.ru. Fri .
"Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation". United States. doi:10.1134/S1063776115050179.
```

```
@article{osti_22472252,
```

title = {Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation},

author = {Ruban, V. P., E-mail: ruban@itp.ac.ru},

abstractNote = {The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.},

doi = {10.1134/S1063776115050179},

journal = {Journal of Experimental and Theoretical Physics},

issn = {1063-7761},

number = 5,

volume = 120,

place = {United States},

year = {2015},

month = {5}

}