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On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on Symmetric Space

Gerdjikov, Vladimir and Grahovski, Georgi and Mikhailov, Alexander (2012) 'On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on Symmetric Space.' Journal of Geometry and Symmetry in Physics, 25 (MARCH). pp. 23-55. ISSN 1312-5192

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Abstract

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is ℤ2× ℤ2reduced 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.

Item Type: Article
Additional Information: 27 pages, 7 figures, LaTeX
Uncontrolled Keywords: nlin.SI; math-ph; math.MP
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 02 Feb 2015 10:13
Last Modified: 15 Jan 2022 00:39
URI: http://repository.essex.ac.uk/id/eprint/11675

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