Proceedings of the International Conference on Geometry, Integrability and Quantization

Breather Solutions of N-Wave Equations

Vladimir Gerdjikov and Tihomir Valchev

Abstract

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.

Article information

Source
Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Manuel de León, eds. (Sofia: Softex, 2007), 184-200

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436792828

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

Mathematical Reviews number (MathSciNet)
MR2341203

Zentralblatt MATH identifier
1123.35342

Citation

Gerdjikov, Vladimir; Valchev, Tihomir. Breather Solutions of N-Wave Equations. Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, 184--200, Softex, Sofia, Bulgaria, 2007. doi:10.7546/giq-8-2007-184-200. https://projecteuclid.org/euclid.pgiq/1436792828


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