Hamiltonian Structure of Benney Type Hydrodynamic and Boltzmann-Vlasov Kinetic Equations on an Axis and Some Applications to Manufacturing Science

Document Type

Article

Publication Date

1-1-1999

Abstract

Some years ago Zakharov and Gibbon observed a very nice relation between the Benney type equation in hydrodynamics and the Vlasov equation of kinetic theory. These equations are generalized and put into the framework of infinite-dimensional Lie algebras associated to Lie algebra structures on rings of functions on finite-dimensional manifolds. This gives rise to a complete description of the Hamiltonian structure of both types of equations under consideration. In particular, their Lax type representations together with an infinite involutive hierarchy of conservation laws are obtained in an exact form. Some applications to chaotic manyparticle dynamical systems, turbulent fluid flows and swept volume analysis are considered.

Identifier

0344279352 (Scopus)

Publication Title

Open Systems and Information Dynamics

External Full Text Location

https://doi.org/10.1023/a:1009642025051

ISSN

12301612

First Page

335

Last Page

374

Issue

4

Volume

6

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