Solitons in the duality-based matrix model

TL;DR

This paper investigates soliton solutions within a duality-based matrix model, identifying types of solutions and their limitations as the system size approaches infinity, with implications for understanding soliton behavior in such models.

Contribution

It introduces and characterizes soliton solutions in the duality-based matrix model, including their types and the limitations on finite soliton configurations at large scales.

Findings

Two types of soliton solutions identified: one soliton-antisoliton and periodic with infinite solitons.

Finite numbers of solitons cannot exist at finite distances as the system size becomes infinite.

No finite number of delta-function solitons exists in the singular limit.

Abstract

We analyze soliton solutions in the duality-based matrix model. There are two types of solution, a one soliton-antisoliton solution (with the constant boundary condition at infinity) and a periodic solution with an infinite number of solitons. It is shown that there is no finite number $ (n > 1) $ of solitons at finite distances in the limit when the length of the box tends to infinity. Particularly, there is no finite number of $ \delta - $ function solitons in the singular limit.