等涡量深水重力-毛细波非线性Schrödinger方程

IF 1 4区工程技术 Q4 MECHANICS

Fluid Dynamics Pub Date : 2023-05-02 DOI:10.1134/S0015462822601851

M. I. Shishina

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引用次数: 1

摘要

考虑了以自由表面和无限深平面底部为界的等涡量深水表面重力-毛细波。从考虑表面张力的保形变量的隐式精确非线性积分微分方程组中导出了一个非线性Schrödinger方程。在推导非线性Schrödinger方程时，考虑了平均流的作用。研究了非线性Schrödinger方程的调制不稳定性。得到了表示“第九波”型孤子的非线性Schrödinger方程的孤子解。

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A Nonlinear Schrödinger Equation for Gravity-Capillary Waves on Deep Water with Constant Vorticity

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.

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来源期刊

Fluid Dynamics MECHANICS-PHYSICS, FLUIDS & PLASMAS

CiteScore

1.30

自引率

22.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Fluid Dynamics is an international peer reviewed journal that publishes theoretical, computational, and experimental research on aeromechanics, hydrodynamics, plasma dynamics, underground hydrodynamics, and biomechanics of continuous media. Special attention is given to new trends developing at the leading edge of science, such as theory and application of multi-phase flows, chemically reactive flows, liquid and gas flows in electromagnetic fields, new hydrodynamical methods of increasing oil output, new approaches to the description of turbulent flows, etc.