Gerdjikov, V, Grahovski, G, Valchev, T et al. (1 more author) (2012) On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on Su(3)/S(U(1) × U(2)) Symmetric Space. Journal of Geometry and Symmetry in Physics, 25. 23 - 55. ISSN 1312-5192
Abstract
We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is ℤ × ℤ reduced and can be naturally associated with the symmetric space SU(3)/S(U(1) × 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 → ± ∞ we analyze the interactions of quadruplet solitons.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | nlin.SI; nlin.SI; math-ph; math.MP |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Sep 2014 09:09 |
Last Modified: | 03 Nov 2016 03:13 |
Status: | Published |
Publisher: | Bulgarian Academy of Sciences |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:74750 |