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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
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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.

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V. S. Gerdjikov, G. G. Grahovski, R. I. Ivanov, N. A. Kostov. 2001-11-05. N-wave interactions related to simple Lie algebras. Z_2- reductions and soliton solutions. https://doi.org/10.1088/0266-5611%2F17%2F4%2F328

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