N-Wave Equations with Orthogonal Algebras: Z₂ and Z₂ × Z₂ Reductions and Soliton Solutions

• Дата: 2007
• Автори: Gerdjikov, V.S., Kostov, N.A., Valchev, T.I.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2007
• Назва видання: Symmetry, Integrability and Geometry: Methods and Applications
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/147823
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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.

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.