AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS

被引：2923

作者：

CAMASSA, R ^{[1
]}

HOLM, DD ^{[1
]}

机构：

[1] LOS ALAMOS NATL LAB,CTR NONLINEAR STUDIES,LOS ALAMOS,NM 87545

来源：

PHYSICAL REVIEW LETTERS | 1993年 / 71卷 / 11期

关键词：

D O I：

10.1103/PhysRevLett.71.1661

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We derive a new completely integrable dispersive shallow water equation that is bi-Hamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in the Hamiltonian for Euler's equations in the shallow water regime. The soliton solution for this equation has a limiting form that has a discontinuity in the first derivative at its peak.

引用

页码：1661 / 1664

页数：4

共 13 条

[1]

Ablowitz M. J., 1981, SOLITONS INVERSE SCA

[2] MODEL EQUATIONS FOR LONG WAVES IN NONLINEAR DISPERSIVE SYSTEMS [J].

BENJAMIN, TB ;

BONA, JL ;

MAHONY, JJ .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 272 (1220) :47-+

[3] DISPERSIVE BAROTROPIC EQUATIONS FOR STRATIFIED MESOSCALE OCEAN DYNAMICS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICA D, 1992, 60 (1-4) :1-15

[4] STABILITY OF FORCED STEADY SOLITARY WAVES [J].

CAMASSA, R ;

WU, TYT .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1991, 337 (1648) :429-466

[5]

CAMASSA R, IN PRESS

[6] NUMERICAL AND THEORETICAL-STUDY OF CERTAIN NON-LINEAR WAVE PHENOMENA [J].

FORNBERG, B ;

WHITHAM, GB .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1978, 289 (1361) :373-404

[7]

Gelfand I., 1979, FUNCT ANAL APPL+, V13, P248, DOI 10.1007/BF01078363

[8] DERIVATION OF EQUATIONS FOR WAVE-PROPAGATION IN WATER OF VARIABLE DEPTH [J].

GREEN, AE ;

NAGHDI, PM .

JOURNAL OF FLUID MECHANICS, 1976, 78 (NOV23) :237-246

[9] HAMILTONIAN-STRUCTURE FOR TWO-DIMENSIONAL HYDRODYNAMICS WITH NONLINEAR DISPERSION [J].

HOLM, DD .

PHYSICS OF FLUIDS, 1988, 31 (08) :2371-2373

[10] UNIDIRECTIONALIZATION OF HAMILTONIAN WAVES [J].

OLVER, PJ .

PHYSICS LETTERS A, 1988, 126 (8-9) :501-506

← 1 2 →