# A uniform approach to soliton cellular automata using rigged configurations

## TL;DR

This paper presents a unified framework for soliton cellular automata using rigged configurations, providing proofs for soliton behavior, scattering, and phase shifts in various cases, enhancing theoretical understanding.

## Contribution

It introduces a uniform approach to analyze soliton cellular automata with rigged configurations, covering cases previously studied separately.

## Key findings

- Rigged configurations describe solitons and their interactions.
- Proofs of soliton scattering and phase shifts in specific automata cases.
- Unified theoretical framework for soliton cellular automata.

## Abstract

For soliton cellular automata, we give a uniform description and proofs of the solitons, the scattering rule of two solitons, and the phase shift using rigged configurations in a number of special cases. In particular, we prove these properties for the soliton cellular automata using $B^{r,1}$ when $r$ is adjacent to $0$ in the Dynkin diagram or there is a Dynkin diagram automorphism sending $r$ to $0$.