Classification of integrable Volterra type lattices on the sphere. Isotropic case

TL;DR

This paper classifies integrable isotropic vector Volterra lattices on the sphere using symmetry methods, revealing mostly new equations and discussing their symplectic structures and related PDEs of NLS-type.

Contribution

It provides a comprehensive classification of integrable isotropic vector Volterra lattices on the sphere, including new equations and their symplectic structures.

Findings

List of mainly new integrable lattices

Analysis of symplectic structures

Associated PDEs of vector NLS-type

Abstract

The symmetry approach is used for classification of integrable isotropic vector Volterra lattices on the sphere. The list of integrable lattices consists mainly of new equations. Their symplectic structure and associated PDE of vector NLS-type are discussed.