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N-wave interactions related to simple Lie algebras. Z_2- reductions and soliton solutions | | V. S. Gerdjikov
; G. G. Grahovski
; R. I. Ivanov
; N. A. Kostov
; | | Date: |
16 Sep 2000 | | Journal: | Inverse problems, 17 (2001), 999-1015 | | Subject: | Exactly Solvable and Integrable Systems | nlin.SI | | Affiliation: | Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria), G. G. Grahovski (Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria), R. I. Ivanov, (Department of Mathematical Physics, National University of Ireland-Galway, Galway, | | 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 analyzed. 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 to each soliton solution one can relate a (semi-)simple subalgebra of g. We illustrate our results by 4-wave equations related to so(5) which find applications in Stockes-anti-Stockes wave generation. | | Source: | arXiv, nlin.SI/0009034 | | Services: | Forum | Review | PDF | Favorites | |
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