Toda lattice with constraint of type B

TL;DR

This paper introduces a new integrable hierarchy derived from the 2D Toda lattice by imposing a constraint, linking it to the BKP hierarchy and providing algebraic-geometrical solutions using Riemann and Prym theta-functions.

Contribution

It defines a novel constrained subhierarchy of the 2D Toda lattice and constructs its algebraic-geometrical solutions, expanding the understanding of integrable systems.

Findings

New integrable hierarchy introduced

Connection to the BKP hierarchy established

Explicit algebraic-geometrical solutions constructed

Abstract

We introduce a new integrable hierarchy of nonlinear differential-difference equations which is a subhierarchy of the 2D Toda lattice defined by imposing a constraint to the Lax operators of the latter. The 2D Toda lattice with the constraint can be regarded as a discretization of the BKP hierarchy. We construct its algebraic-geometrical solutions in terms of Riemann and Prym theta-functions.