# Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy

@article{Brunelli1996HamiltonianSF, title={Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy}, author={J. C. Brunelli}, journal={Reviews in Mathematical Physics}, year={1996}, volume={8}, pages={1041-1053} }

We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so-called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system.

## 12 Citations

Lagrangian Approach to Dispersionless KdV Hierarchy

- Physics, Mathematics
- 2007

We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as…

Infinite-dimensional 3-algebra and integrable system

- Physics, Mathematics
- 2012

A bstractThe relation between the infinite-dimensional 3-algebras and the dispersionless KdV hierarchy is investigated. Based on the infinite-dimensional 3-algebras, we derive two compatible Nambu…

Integrable dispersionless KdV hierarchy with sources

- Mathematics, Physics
- 2006

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. A hodograph solution for the dispersionless…

Dispersionless limit of integrable models

- Physics
- 2000

Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these…

A Lax equation for the non-linear sigma model

- Physics
- 2002

We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges…

Properties of Moyal-Lax representation

- Physics
- 2001

Abstract The properties of standard and the nonstandard Moyal–Lax representations are systematically investigated. It is shown that the Moyal–Lax equation can be interpreted as a Hamiltonian equation…

Dispersionless fermionic KdV

- Physics, Mathematics
- 1999

Abstract We analyze the dispersionless limits of the Kupershmidt equation, the SUSY KdV-B equation and the SUSY KdV equation. We present the Lax description for each of these models and bring out…

ON THE INTEGRABILITY OF A CLASS OF MONGE–AMPÈRE EQUATIONS

- Physics, Mathematics
- 1999

We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge–Ampere equations. The connection between these equations and the equations of hydrodynamical type give…

A unitary matrix model for q-deformed Plancherel growth

- PhysicsNuclear Physics B
- 2021

In this paper we construct a unitary matrix model that captures the asymptotic growth of Young diagrams under q-deformed Plancherel measure. The matrix model is a q analog of Gross-Witten-Wadia (GWW)…

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