Lump Scattering on a Torus

TL;DR

This paper investigates head-on collisions of solitons on a flat torus in the $CP^1$ model, revealing 90-degree scattering and singularity formation through numerical simulations.

Contribution

It demonstrates 90-degree scattering of charge-two lumps in the $CP^1$ model on a torus using elliptic functions, highlighting singularity phenomena.

Findings

Charge-two lumps scatter at 90 degrees.

Singularity formation occurs during collisions.

Numerical simulations confirm theoretical predictions.

Abstract

Head-on collisions between two solitons in the pure $CP^1$ model on a flat torus are investigated via numerical simulations. The charge-two lumps, written out in terms of Weierstrass' elliptic $\wp$-function, are found to scatter at 90$^{\circ}$. The phenomenon of singularity formation is also seen.