#### Document Type

Article

#### Rights

This item is available under a Creative Commons License for non-commercial use only

#### Disciplines

Applied mathematics

#### Abstract

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z2 \times Z2 reduced and is naturally associated with the symmetric space 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; their velocities and their amplitudes are time dependent. Calculating the asymptotics of the N-soliton solutions for t \rightarrow \pm \infty we analyze the interactions of quadruplet solitons.

#### DOI

http://doi.org10.21427/6dpx-8h33

#### Recommended Citation

Gerdjikov, V.S., Grahovski, G.G., Mikhailov, A.V., Valchev, T.I. Soliton Interactions for a Hierarchy of Generalized Heisenberg Ferromagnetic Models on SU(3)/S(U(1) $\times$ U(2)) Symmetric Space Journal of Geometry and Symmetry in Physics, 25 (2012), 23 - 55 (E-print: arXiv:1201.0534v1 [nlin.SI]) doi : 10.21427/6dpx-8h33

#### Funder

SFI, Royalsoc

#### Included in

Dynamic Systems Commons, Mathematics Commons, Non-linear Dynamics Commons, Partial Differential Equations Commons

## Publication Details

Journal of Geometry and Symmetry in Physics, 25 (2012), 23 - 55

(E-print: arXiv:1201.0534v1 [nlin.SI])