Email this article A Nonlinear Schrеdinger Equation for Gravity-Capillary Waves on Deep Water with Constant Vorticit
- Authors: Shishina M.I.1
-
Affiliations:
- Nizhny Novgorod Planetarium named after G.M. Grechko
- Issue: No 2 (2023)
- Pages: 20-32
- Section: Articles
- URL: https://journals.rcsi.science/1024-7084/article/view/135062
- DOI: https://doi.org/10.31857/S0568528122600321
- EDN: https://elibrary.ru/DUFTMO
- ID: 135062
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Abstract
The surface gravity-capillary waves on deep water with constant vorticity in the region
bounded by the free surface and the infinitely deep plane bottom are considered. A nonlinear Schrödinger equation is derived from a system of exact nonlinear integro-differential equations in conformal variables written in the implicit form taking into account surface tension. In deriving the nonlinear Schrödinger equation, the role of the mean flow is taken into account. The nonlinear Schrödinger equation is investigated for modulation instability. A soliton solution of the nonlinear Schrödinger equation that represents a soliton of the “ninth wave” type is obtained. bounded by the free surface and the infinitely deep plane bottom are considered. A nonlinear Schrödinger equation is derived from a system of exact nonlinear integro-differential equations in conformal
variables written in the implicit form taking into account surface tension. In deriving the nonlinear Schrödinger equation, the role of the mean flow is taken into account. The nonlinear Schrödinger equation is investigated for modulation instability. A soliton solution of the nonlinear Schrödinger equation that represents a soliton of the “ninth wave” type is obtained.
About the authors
M. I. Shishina
Nizhny Novgorod Planetarium named after G.M. Grechko
Author for correspondence.
Email: java-jsp@yandex.ru
Nizhny Novgorod, Russia
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