N-Wave Equations with Orthogonal Algebras: Z₂ and Z₂ × Z₂ Reductions and Soliton Solutions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
N-Wave Equations with Orthogonal Algebras: Z₂ and Z₂ × Z₂ Reductions and Soliton Solutions
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| Creator |
Gerdjikov, V.S.
Kostov, N.A. Valchev, T.I. |
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| Description |
We consider N-wave type equations related to the orthogonal algebras obtained from the generic ones via additional reductions. The first Z₂-reduction is the canonical one. We impose a second Z₂-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 B₂ algebra with a canonical Z₂ reduction.
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| Date |
2019-02-16T08:53:20Z
2019-02-16T08:53:20Z 2007 |
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| Type |
Article
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| Identifier |
N-Wave Equations with Orthogonal Algebras: Z₂ and Z₂ × Z₂ Reductions and Soliton Solutions / V.S. Gerdjikov, N.A. Kostov, T.I. Valchev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 37K15; 17B70; 37K10; 17B80 http://dspace.nbuv.gov.ua/handle/123456789/147823 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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