Weierstrass P-lumps

TL;DR

This paper numerically investigates the dynamics of two solitons in a (2+1)D $CP^1$ model on a torus, revealing behaviors like splitting, right-angle scattering, and motion reversal, using elliptic functions of Weierstrass.

Contribution

It provides new numerical insights into soliton interactions in the $CP^1$ model on a torus, focusing on static initial conditions and employing elliptic functions.

Findings

Solitons exhibit splitting and scattering behaviors.

Right-angle scattering observed in soliton interactions.

Motion reversal occurs in various configurations.

Abstract

We present our results of a numerical investigation of the behaviour of a system of two solitons in the (2+1) dimensional $CP^1$ model on a torus. Defined by the elliptic function of Weierstrass, and working in the Skyrme version of the model, the soliton lumps exhibit splitting, scattering at right angles and motion reversal in the various configurations considered. The work is restricted to systems with no initial velocity.