Dressed Elliptic String Solutions on RxS^2

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.

arXiv comment47 pages, 2 figures

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Cited by in corpus (6)

• Salient Features of Dressed Elliptic String Solutions on $\mathbb{R}\times$S${}^2$
• Stability Analysis of Classical String Solutions and the Dressing Method
• The Dressing Method as Non Linear Superposition in Sigma Models
• Dressed Minimal Surfaces in AdS${}_4$
• Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model
• Novel aspects of integrability for NLSMs in symmetric spaces