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NWave Equations with Orthogonal Algebras: Z_2 and Z_2 imes Z_2 Reductions and Soliton Solutions  Vladimir S. Gerdjikov
; Nikolay A. Kostov
; Tihomir I. Valchev
;  Date: 
3 Mar 2007  Journal:  SIGMA 3 (2007), 039, 19 pages  Subject:  Exactly Solvable and Integrable Systems  Abstract:  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 ZakharovShabat dressing method. We also briefly discuss the different types of onesoliton solutions. Especially rich are the types of onesoliton 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 sineGordon case, which allows two types of solitons: kinks and breathers. A new physical system, describing Stokesanti Stokes Raman scattering is obtained. It is represented by a 4wave equation related to the ${f B}_2$ algebra with a canonical $mathbb{Z}_2$ reduction.  Source:  arXiv, nlin/0703002  Services:  Forum  Review  PDF  Favorites 


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