Two-dimensional Ultra-Toda integrable mappings and chains (Abelian case)

TL;DR

This paper introduces a new class of integrable mappings and chains in two dimensions, providing explicit (1+2) systems invariant under these transformations and expressing soliton solutions via semisimple algebra representations.

Contribution

It presents a novel class of 2D integrable mappings and chains, along with explicit (1+2) systems and soliton solutions based on semisimple algebra representations.

Findings

New class of integrable mappings and chains introduced.

Explicit (1+2) integrable systems derived.

Soliton solutions expressed through semisimple algebra representations.

Abstract

The new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are represented in explicit form. Soliton like solutions of them are represented in terms of matrix elements of fundamental representations of semisimple A_n algebras for a given group element.