Toda and Volterra Lattice Equations from Discrete Symmetries of KP Hierarchies

Abstract

The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson currents of KP hierarchy are being associated with sites of the corresponding chain by successive actions of discrete symmetry.

12 pgs, LaTeX, IFT-P.041/93

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Cited by in corpus (12)

• The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra
• The integrable hierarchy constructed from a pair of KdV-type hierarchies and its associated $W$ algebra
• Extension of the discrete KP hierarchy
• A class of integrable lattices and KP hierarchy
• On Discrete Symmetries of the Multi-Boson KP Hierarchies
• Hamiltonian Structures of the Multi-Boson KP Hierarchies, Abelianization and Lattice Formulation
• Gauge Symmetry Origin of Bäcklund Transformations for Painlevé Equations
• Reductions of the Volterra and Toda chains
• On Rational Solutions of Dressing Chains of Even Periodicity
• Integrable Origins of Higher Order Painleve Equations
• On the symmetric formulation of the Painleve IV equation
• The Lattice Equations of the Toda Type with an Interaction between a Few Neighborhoods