https://doi.org/10.1140/epjc/s10052-018-6129-x
Regular Article - Theoretical Physics
Dressed elliptic string solutions on 
1
Department of Physics, National and Kapodistrian University of Athens, University Campus, Zografou, 15784, Athens, Greece
2
NCSR “Demokritos”, Institute of Nuclear and Particle Physics, Aghia Paraskevi, 15310, Attiki, Greece
3
Department of Physics, School of Applied Mathematics and Physical Sciences, National Technical University, 15780, Athens, Greece
* e-mail: mitsoula@central.ntua.gr
Received:
26
June
2018
Accepted:
1
August
2018
Published online:
21
August
2018
We obtain classical string solutions on 
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 Bäcklund 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.
© The Author(s), 2018
