On vector analogs of the modified Volterra lattice

TL;DR

This paper introduces a new vector generalization of the modified Volterra lattice, explores its integrability properties, and presents explicit soliton and breather solutions, connecting it with other integrable systems.

Contribution

It is the first study of one of the vector generalizations of the modified Volterra lattice, including its zero curvature, Bäcklund transformations, and explicit solutions.

Findings

First analysis of a vector generalization of the modified Volterra lattice.

Explicit soliton and breather solutions derived.

Connections established with other integrable equations.

Abstract

Modified Volterra lattice admits two vector generalizations. One of them is studied for the first time. The zero curvature representations, B\"acklund transformations, nonlinear superposition principle and the simplest explicit solutions of soliton and breather type are presented for both vector lattices. The relations with some other integrable equations are established.