Toda and Volterra Lattice Equations from Discrete Symmetries of KP Hierarchies

TL;DR

This paper constructs discrete Toda and Volterra lattice models from KP hierarchies using discrete symmetries that preserve Hamiltonian structures, linking KP currents to lattice sites.

Contribution

It introduces a novel method of deriving discrete lattice models from continuum KP hierarchies via symmetry transformations.

Findings

Discrete models of Toda and Volterra chains are derived from KP hierarchies.

Discrete symmetry preserves the Hamiltonian structure of the models.

KP currents are associated with lattice sites through symmetry actions.

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.