Hamiltonian Structures of Reductions of the Benney System

被引：8

作者：

Gibbons, John ^{[1
]}

Lorenzoni, Paolo ^{[2
]}

Raimondo, Andrea ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2009年 / 287卷 / 01期

关键词：

HYDRODYNAMIC TYPE; POISSON BRACKETS; EQUATIONS;

D O I：

10.1007/s00220-008-0686-z

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show how to construct the Hamiltonian structures of any reduction of the Benney chain (dispersionless KP). The construction follows the scheme suggested by Ferapontov, leading in general to nonlocal Hamiltonian structures. In some special cases these reduce to local structures. All the geometric objects which define the Poisson bracket, the metric, connection and Riemann curvature, are obtained explicitly, in terms of the n-parameter family of conformal maps associated with the reduction.

引用

页码：291 / 322

页数：32

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