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VOL. 8 | 2007 Breather Solutions of N-Wave Equations
Vladimir Gerdjikov, Tihomir Valchev

Editor(s) Ivaïlo M. Mladenov, Manuel de León


We consider $N$-wave type equations related to symplectic and orthogonal algebras. We obtain their soliton solutions in the case when two different $\mathbb{Z}_2$ reductions (or equivalently one $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$-reduction) are imposed. For that purpose we apply a particular case of an auto-Bäcklund transformation – the Zakharov–Shabat dressing method. The corresponding dressing factor is consistent with the $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$-reduction. These soliton solutions represent $N$-wave breather-like solitons. The discrete eigenvalues of the Lax operators connected with these solitons form “quadruplets” of points which are symmetrically situated with respect to the coordinate axes.


Published: 1 January 2007
First available in Project Euclid: 13 July 2015

zbMATH: 1123.35342
MathSciNet: MR2341203

Digital Object Identifier: 10.7546/giq-8-2007-184-200

Rights: Copyright © 2007 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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