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2012 On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on ${\rm SU(3)/S(U(1)\times U(2))}$ Symmetric Space
Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valchev
J. Geom. Symmetry Phys. 25: 23-55 (2012). DOI: 10.7546/jgsp-25-2012-23-55

Abstract

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator $L$. The Lax representation is $\mathbb{Z}_2\times\mathbb{Z}_2$ reduced and can be naturally associated with the symmetric space ${\rm SU(3)/S(U(1)\times U(2))}$. The simplest nontrivial equation in the hierarchy is a generalization of Heisenberg ferromagnetic model. We construct the $N$-soliton solutions for an arbitrary member of the hierarchy by using the Zakharov-Shabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The one-soliton solutions of NLEEs with even and odd dispersion laws have different properties. In particular, the one-soliton solutions for NLEEs with even dispersion laws are not traveling waves while their velocities and amplitudes are time dependent. Calculating the asymptotics of the $N$-soliton solutions for $t\to\pm\infty$ we analyze the interactions of quadruplet solitons.

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Vladimir Gerdjikov. Georgi Grahovski. Alexander Mikhailov. Tihomir Valchev. "On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on ${\rm SU(3)/S(U(1)\times U(2))}$ Symmetric Space." J. Geom. Symmetry Phys. 25 23 - 55, 2012. https://doi.org/10.7546/jgsp-25-2012-23-55

Information

Published: 2012
First available in Project Euclid: 25 May 2017

zbMATH: 1259.82127
MathSciNet: MR2976793
Digital Object Identifier: 10.7546/jgsp-25-2012-23-55

Rights: Copyright © 2012 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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