Solitons with nested structure over finite fields

TL;DR

This paper introduces a novel finite field solitonic system resembling box-ball systems, featuring nested, fractal-like one-soliton solutions, polynomial descriptions, and stable multi-soliton interactions demonstrated through simulations.

Contribution

It presents a new finite field solitonic system with polynomial formulation and nested fractal-like solutions, expanding the understanding of soliton dynamics in discrete algebraic settings.

Findings

One-soliton solutions have nested fractal-like structures.

Numerical simulations show stable propagation and collision of solitons.

The system is described by polynomials, a novel approach.

Abstract

We propose a solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. The one-soliton solutions of the system, which have nested structures similar to fractals, are also proved. The solitonic system in this paper is described by polynomials, which seems to be novel. Furthermore, in spite of such complex internal structures, numerical simulations exhibit stable propagations before and after collisions among multiple solitons with preserving their patterns.