N-wave interactions related to simple Lie algebras. Z_2- reductions and soliton solutions

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.

18 pages, 1 figure, LaTeX 2e, IOP-style; More clear exposition. Introduction and Section 5 revised. Some typos are corrected

References in corpus (2)

• Complete Integrability of Completely Integrable Systems
• INVERSE SCATTERING TRANSFORM ANALYSIS OF STOKES-ANTI-STOKES STIMULATED RAMAN SCATTERING

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