N-Wave Equations with Orthogonal Algebras: Z_2 and Z_2 \times Z_2 Reductions and Soliton Solutions
| dc.creator | Gerdjikov, Vladimir S. | |
| dc.creator | Kostov, Nikolay A. | |
| dc.creator | Valchev, Tihomir I. | |
| dc.date | 2007-03-03 | |
| dc.date.accessioned | 2026-07-07T09:34:43Z | |
| dc.date.available | 2026-07-07T09:34:43Z | |
| dc.description | We consider $N$-wave type equations related to the orthogonal algebras obtained from the generic ones via additional reductions. The first $\mathbb{Z}_2$-reduction is the canonical one. We impose a second $\mathbb{Z}_2$-reduction and consider also the combined action of both reductions. For all three types of $N$-wave equations we construct the soliton solutions by appropriately modifying the Zakharov-Shabat dressing method. We also briefly discuss the different types of one-soliton solutions. Especially rich are the types of one-soliton solutions in the case when both reductions are applied. This is due to the fact that we have two different configurations of eigenvalues for the Lax operator $L$: doublets, which consist of pairs of purely imaginary eigenvalues, and quadruplets. Such situation is analogous to the one encountered in the sine-Gordon case, which allows two types of solitons: kinks and breathers. A new physical system, describing Stokes-anti Stokes Raman scattering is obtained. It is represented by a 4-wave equation related to the ${\bf B}_2$ algebra with a canonical $\mathbb{Z}_2$ reduction. | |
| dc.description | This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/nlin/0703002 | |
| dc.identifier | http://arxiv.org/abs/nlin/0703002 | |
| dc.identifier | SIGMA 3 (2007), 039, 19 pages | |
| dc.identifier | doi:10.3842/SIGMA.2007.039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159590 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | Mathematical Physics | |
| dc.title | N-Wave Equations with Orthogonal Algebras: Z_2 and Z_2 \times Z_2 Reductions and Soliton Solutions | |
| dc.type | text |