forgot password?
register here
Research articles
  search articles
  reviews guidelines
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
Members: 2895
Articles: 1'996'896
Articles rated: 2574

22 September 2020
  » arxiv » nlin/0703002

 Article overview

N-Wave 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
AbstractWe 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 ${f B}_2$ algebra with a canonical $mathbb{Z}_2$ reduction.
Source arXiv, nlin/0703002
Services Forum | Review | PDF | Favorites   
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
of broad interest:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser CCBot/2.0 (
» my Online CV
» Free

News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2020 - Scimetrica