Asymptotic integrability of water waves

被引：111

作者：

Fokas, AS

Liu, QM

机构：

[1] CLARKSON UNIV, INST NONLINEAR STUDIES, POTSDAM, NY 13699 USA

[2] CLARKSON UNIV, DEPT MATH & COMP SCI, POTSDAM, NY 13699 USA

来源：

PHYSICAL REVIEW LETTERS | 1996年 / 77卷 / 12期

关键词：

D O I：

10.1103/PhysRevLett.77.2347

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The asymptotic integrability of the idealized water waves is formally established. Namely, it is shown that in the small amplitude, long wave limit there exists an explicit transformation which maps these equations to a system of two integrable equations. It is also shown that the concepts of master symmetries and of bi-Hamiltonian structures can be used to obtain similar results for other physical systems.

引用

页码：2347 / 2351

页数：5

共 17 条

[1] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS
CAMASSA, R
HOLM, DD
[J]. PHYSICAL REVIEW LETTERS, 1993, 71 (11) : 1661 - 1664
[2] THE HIERARCHY OF THE BENJAMIN-ONO-EQUATION
FOKAS, AS
FUCHSSTEINER, B
[J]. PHYSICS LETTERS A, 1981, 86 (6-7) : 341 - 345
[3] ON A CLASS OF PHYSICALLY IMPORTANT INTEGRABLE EQUATIONS
FOKAS, AS
[J]. PHYSICA D-NONLINEAR PHENOMENA, 1995, 87 (1-4) : 145 - 150
[4] THE KORTEWEG-DE VRIES EQUATION AND BEYOND
FOKAS, AS
[J]. ACTA APPLICANDAE MATHEMATICAE, 1995, 39 (1-3) : 295 - 305
[5] FOKAS AS, IN PRESS ASYMPTOTIC
[6] FOKAS AS, IN PRESS INVERSE ACO
[7] THE LIE-ALGEBRA STRUCTURE OF NON-LINEAR EVOLUTION-EQUATIONS ADMITTING INFINITE DIMENSIONAL ABELIAN SYMMETRY GROUPS
FUCHSSTEINER, B
[J]. PROGRESS OF THEORETICAL PHYSICS, 1981, 65 (03): : 861 - 876
[8] SYMPLECTIC STRUCTURES, THEIR BACKLUND-TRANSFORMATIONS AND HEREDITARY SYMMETRIES
FUCHSSTEINER, B
FOKAS, AS
[J]. PHYSICA D, 1981, 4 (01): : 47 - 66
[9] METHOD FOR SOLVING KORTEWEG-DEVRIES EQUATION
GARDNER, CS
GREENE, JM
KRUSKAL, MD
MIURA, RM
[J]. PHYSICAL REVIEW LETTERS, 1967, 19 (19) : 1095 - &
[10] HIGHER-ORDER WATER-WAVE EQUATION AND METHOD FOR SOLVING IT
KAUP, DJ
[J]. PROGRESS OF THEORETICAL PHYSICS, 1975, 54 (02): : 396 - 408

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