Inverse scattering method for a soliton cellular automaton

TL;DR

This paper develops an inverse scattering method for solving initial value problems in a soliton cellular automaton, linking it with rigged configurations and providing a new fermionic character formula interpretation.

Contribution

It introduces an inverse scattering approach using rigged configurations as scattering data for the automaton, connecting integrable systems with combinatorial objects.

Findings

Established a set of action-angle variables for the automaton.

Linked the variables with rigged configurations from Bethe ansatz.

Derived a new fermionic character formula interpretation.

Abstract

A set of action-angle variables for a soliton cellular automaton is obtained. It is identified with the rigged configuration, a well-known object in Bethe ansatz. Regarding it as the set of scattering data an inverse scattering method to solve initial value problems of this automaton is presented. By considering partition functions for this system a new interpretation of a fermionic character formula is obtained.