Dressed Elliptic String Solutions on RxS^2

TL;DR

This paper constructs new classical string solutions on RxS^2 using the dressing method applied to elliptic solutions, revealing bifurcations and a geometric interpretation involving epicycles.

Contribution

It introduces a novel application of the dressing method with a simple pole structure to generate and analyze dressed elliptic string solutions on RxS^2.

Findings

Dressed solutions exhibit bifurcation at specific moduli.

Dressed strings can be visualized as epicycles around seed solutions.

The radius of the epicycle relates to the dressing poles.

Abstract

We obtain classical string solutions on RxS^2 by applying the dressing method on string solutions with elliptic Pohlmeyer counterparts. This is realized through the use of the simplest possible dressing factor, which possesses just a pair of poles lying on the unit circle. The latter is equivalent to the action of a single Backlund transformation on the corresponding sine-Gordon solutions. The obtained dressed elliptic strings present an interesting bifurcation of their qualitative characteristics at a specific value of a modulus of the seed solutions. Finally, an interesting generic feature of the dressed strings, which originates from the form of the simplest dressing factor and not from the specific seed solution, is the fact that they can be considered as drawn by an epicycle of constant radius whose center is running on the seed solution. The radius of the epicycle is directly related to the location of the poles of the dressing factor.