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N-wave interactions related to simple lie algebras. ℤ2-reductions and soliton solutions

Gerdjikov, V S
Grahovski, G G
Ivanov, R I
Kostov, N A
Repository DOI
Publication Date
2001-07-23
Type
Article
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Citation
Gerdjikov, V S; Grahovski, G G; Ivanov, R I; Kostov, N A (2001). N-wave interactions related to simple lie algebras. ℤ2-reductions and soliton solutions. Inverse Problems 17 (4), 999-1015
Abstract
The reductions of the integrable N-wave type equations solvable by the inverse scattering method with the generalized Zakharov-Shabat systems L and related to some simple Lie algebra g are analysed. The Zakharov-Shabat dressing method is extended to the case when g is an orthogonal algebra. Several types of one-soliton solutions of the corresponding N-wave equations and their reductions are studied. We show that one can relate a (semi-)simple subalgebra of g to each soliton solution. We illustrate our results by four-wave equations related to so (5) which find applications in Stokes-anti-Stokes wave generation.
Funder
Publisher
IOP Publishing
Publisher DOI
10.1088/0266-5611/17/4/328
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Attribution-NonCommercial-NoDerivs 3.0 Ireland