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VOL. 13 | 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

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka


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.


Published: 1 January 2012
First available in Project Euclid: 13 July 2015

zbMATH: 1382.82049
MathSciNet: MR3087962

Digital Object Identifier: 10.7546/giq-13-2012-11-42

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


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