Rogue solitons in Heisenberg spin chain

TL;DR

This paper establishes a connection between rogue solitons in the nonlinear Schrödinger equation and similar localized structures in the Heisenberg spin chain, using geometric and dynamical system analogies.

Contribution

It introduces a novel mapping of rogue solitons and breathers from the nonlinear Schrödinger equation to the Heisenberg spin chain, expanding understanding of localized wave phenomena in spin systems.

Findings

Identification of rogue soliton equivalents in spin chains

Mapping of breathers to localized oscillatory modes

Analysis of curvature and torsion dynamics related to rogue waves

Abstract

Following the connection of the non-linear Schr\"{o}dinger 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.