Box-Basket-Ball Systems

TL;DR

The paper introduces the box-basket-ball system, a new discrete solitonic model extending the box-ball system, where balls and baskets behave as fermionic and bosonic particles, respectively, and analyzes their solitons and scattering behavior.

Contribution

It defines a novel integrable system combining fermionic and bosonic particles and classifies its solitons and scattering properties.

Findings

Identification of solitons in the system

Classification of soliton scattering behavior

Extension of the box-ball system to include baskets

Abstract

Using the whurl relation of the first two authors, we define a new discrete solitonic system, which we call the box-basket-ball system, generalizing the box-ball system of Takahashi and Satsuma. In box-basket-ball systems balls may be put either into boxes or into baskets. While boxes stay fixed, both balls and baskets get moved during time evolution. Balls and baskets behave as fermionic and bosonic particles respectively. We classify the solitons of this system, and study their scattering.