The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies

Details The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies

1996-06-05

arxiv.org/abs/hep-th/9606022v1

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, LaTeX

Scientific paper

10.1088/0266-5611/12/6/006

The algebraic and Hamiltonian structures of the multicomponent dispersionless Benney and Toda hierarchies are studied. This is achieved by using a modified set of variables for which there is a symmetry between the basic fields. This symmetry enables formulae normally given implicitly in terms of residues, such as conserved charges and fluxes, to be calculated explicitly. As a corollary of these results the equivalence of the Benney and Toda hierarchies is established. It is further shown that such quantities may be expressed in terms of generalized hypergeometric functions, the simplest example involving Legendre polynomials. These results are then extended to systems derived from a rational Lax function and a logarithmic function. Various reductions are also studied.

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