The classical shallow water equations: Symplectic geometry

J. Cavalcante, H. P. McKean

Research output: Contribution to journalArticle

Abstract

The classical shallow water equations express the change with time of the height h and the velocity ν of a 1-dimensional fluid: νξ νt+ νξ νx+ νh νx=0. νh νx+ νhν νx=0. They possess an infinite number of integrals of motion due to Benney [1973] and can be written in Hamiltonian form relative to a symplectic structure introduced by Manin [1978]. The present paper deals with their complete integrability up to the advent of shocks. This is proved in the small under an extra assumption satisfied by most height-velocity pairs: that hh′ = ± ν′ only at isolated points.

Original languageEnglish (US)
Pages (from-to)253-260
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Volume4
Issue number2
DOIs
StatePublished - 1982

Fingerprint

Symplectic Geometry
Shallow Water Equations
shallow water
Complete Integrability
Hamiltonians
Integrals of Motion
Geometry
Symplectic Structure
geometry
Water
Shock
Express
shock
Fluid
Fluids
fluids
Form

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

The classical shallow water equations : Symplectic geometry. / Cavalcante, J.; McKean, H. P.

In: Physica D: Nonlinear Phenomena, Vol. 4, No. 2, 1982, p. 253-260.

Research output: Contribution to journalArticle

Cavalcante, J. ; McKean, H. P. / The classical shallow water equations : Symplectic geometry. In: Physica D: Nonlinear Phenomena. 1982 ; Vol. 4, No. 2. pp. 253-260.
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