Eur. Phys. J. B (2015) 88: 188
https://doi.org/10.1140/epjb/e2015-60229-8

Regular Article

Rogue waves and breathers in Heisenberg spin chain

¹ Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
² Institute of Mathematical Sciences, IV Cross Road, CIT Campus, Taramani, 600113 Chennai, India
³ Indian Institute of Science Education and Research (IISER) Kolkata, 741246 Mohanpur, India

^a e-mail: aritra.mukhopadhyay@physnet.uni-hamburg.de

Received: 22 March 2015
Received in final form: 8 June 2015
Published online: 22 July 2015

Abstract

Following the connection of the non-linear Schrödinger equation with the continuum Heisenberg spin chain, we find the rogue soliton equivalent in the spin system. The breathers are also mapped to the corresponding space or time localized oscillatory modes, through the moving curve analogy. The spatio-temporal evolution of the curvature and torsion of the curve, underlying these dynamical systems, are explicated to illustrate the localization property of the rogue waves.