N-wave equations with orthogonal algebras: Z2and Z2× Z2reductions and soliton solutions

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creativework.keywordsHamiltonian systems, Solitons
creativework.publisherInstitute of Mathematicsen
dc.contributor.authorGerdjikov V.S.
dc.contributor.authorKostov N.A.
dc.contributor.authorValchev T.I.
dc.date.accessioned2024-07-10T14:27:03Z
dc.date.accessioned2024-07-10T14:48:02Z
dc.date.available2024-07-10T14:27:03Z
dc.date.available2024-07-10T14:48:02Z
dc.date.issued2007-01-01
dc.description.abstractWe 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 B2algebra with a canonical Z2reduction.
dc.identifier.doi10.3842/SIGMA.2007.039
dc.identifier.issn1815-0659
dc.identifier.scopusSCOPUS_ID:84889235929en
dc.identifier.urihttps://rlib.uctm.edu/handle/123456789/295
dc.language.isoen
dc.source.urihttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84889235929&origin=inward
dc.titleN-wave equations with orthogonal algebras: Z2and Z2× Z2reductions and soliton solutions
dc.typeArticle
oaire.citation.volume3
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