Degenerate bi-Hamiltonian structures of hydrodynamic type
type: Item
instance of: scholarly article
title: Degenerate bi-Hamiltonian structures of hydrodynamic type
zbMATH Open document ID: 0963.37062
DOI: 10.1007/BF02551201
published in: Theoretical and Mathematical Physics
publication date: 2000-11-23T00:00:00Z
review text: This paper is devoted to degenerate bi-Hamiltonian Poisson brackets of hydrodynamic type. It is shown that they are bi-Hamiltonian structures of certain dispersionless rational Lax equations and are related to the notion of a degenerate Frobenius manifold (the natural geometric setting in which the bi-Hamiltonian structure of hydrodynamic systems can be understood is the Frobenius manifold).
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K05
zbMATH DE Number: 1535324
zbMATH Keywords: hydrodynamic type
zbMATH Keywords: Lax equation
zbMATH Keywords: bi-Hamiltonian structure
zbMATH Keywords: Frobenius manifold
author: Ian A. B. Strachan
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q4860065
cites work: A simple model of the integrable Hamiltonian equation
cites work: On compatible Poisson structures of hydrodynamic type
cites work: On compatible potential deformations of Frobenius algebras and associativity equations
cites work: Q4382424
cites work: Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
cites work: The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies
cites work: Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
description: scientific article; zbMATH DE number 1535324