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. 2355. ISSN 13125192

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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 Nsoliton solutions for an arbitrary member of the hierarchy by using the ZakharovShabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The onesoliton solutions of NLEEs with even and odd dispersion laws have different properties. In particular, the onesoliton solutions for NLEEs with even dispersion laws are not traveling waves while their velocities and amplitudes are time dependent. Calculating the asymptotics of the Nsoliton solutions for t → ± ∞ we analyze the interactions of quadruplet solitons.
Item Type:  Article 

Additional Information:  27 pages, 7 figures, LaTeX 
Uncontrolled Keywords:  nlin.SI; mathph; 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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