## 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.

Original language | English (US) |
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Pages (from-to) | 335-374 |

Number of pages | 40 |

Journal | Open Systems and Information Dynamics |

Volume | 6 |

Issue number | 4 |

State | Published - Dec 1999 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics