The Hamiltonian structure of the dispersionless Toda hierarchy

Abstract

The Hamiltonian structure of the two-dimensional dispersionless Toda hierarchy is studied, this being a particular example of a system of hydrodynamic type. The polynomial conservation laws for the system turn out, after a change of variable, to be associated with the axially symmetric solutions of the 3-dimensional Laplace equation and this enables a generating function for the Hamiltonian densities to be derived in closed form.

12 pages, latex, no figures

References in corpus (3)

• SDiff(2) Toda equation -- hierarchy, $\tau$ function, and symmetries
• Integrable Generalisations of the 2-dimensional Born Infeld Equation
• Infinite Charge Algebra of Gravitational Instantons

Cited by in corpus (3)

• Integrable Symplectic Trilinear Interaction Terms for Matrix Membranes
• The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies
• Hydrodynamic type integrable equations on a segment and a half-line