Reductions of integrable lattices

TL;DR

This paper introduces a method to derive compatible constraints for integrable lattices using Darboux-KP chain hierarchy and invariant submanifolds, expanding the understanding of integrable lattice reductions.

Contribution

It presents a novel approach to construct constraints for integrable lattices based on Darboux-KP chain hierarchy and invariant submanifolds.

Findings

Constructed classes of constraints compatible with integrable lattices

Provided simple examples illustrating the constraints

Enhanced the theoretical framework for integrable lattice reductions

Abstract

Based on the notion of Darboux-KP chain hierarchy and its invariant submanifolds we construct some class of constraints compatible with integrable lattices. Some simple examples are given.