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

Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov
2012 unpublished
We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z 2 × Z 2 reduced and is 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
more » ... opriately 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 → ±∞ we analyze the interactions of quadruplet solitons.
doi:10.7546/giq-13-2012-11-42 fatcat:kzuxet7vo5bczp2rfxzkmw3xji