A Model Equation for Wavepacket Solitary Waves Arising from Capillary-Gravity Flows

被引：48

作者：

Akers, Benjamin ^{[1
]}

Milewski, Paul A. ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

STUDIES IN APPLIED MATHEMATICS | 2009年 / 122卷 / 03期

关键词：

WATER-WAVES; INFINITE DEPTH; FREE-SURFACE; DEEP-WATER; STABILITY; LUMPS;

D O I：

10.1111/j.1467-9590.2009.00432.x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A model equation governing the primitive dynamics of wave packets near an extremum of the linear dispersion relation at finite wavenumber is derived. In two spatial dimensions, we include the effects of weak variation of the wave in the direction transverse to the direction of propagation. The resulting equation is contrasted with the Kadomtsev-Petviashvilli and Nonlinear Schrodinger (NLS) equations. The model is derived as an approximation to the equations for deep water gravity-capillary waves, but has wider applications. Both line solitary waves and solitary waves which decay in both the transverse and propagating directions-lump solitary waves-are computed. The stability of these waves is investigated and their dynamics are studied via numerical time evolution of the equation.

引用

页码：249 / 274

页数：26

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