Reductions of N-wave interactions related to low-rank simple Lie algebras. I: Z_2- reductions

Abstract

The analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method is an interesting and still open problem. We show how the second order reductions of the N-wave interactions related to low-rank simple Lie algebras g can be embedded also in the Weyl group of g. This allows us to display along with the well known ones a number of new types of integrable N-wave systems. Some of the reduced systems find applications to nonlinear optics.

40 pages, no figures, LaTeX, IOP-style. Section 5 revised. Some typos are corrected

References in corpus (3)

• N-wave interactions related to simple Lie algebras. Z_2- reductions and soliton solutions
• Complete Integrability of Completely Integrable Systems
• INVERSE SCATTERING TRANSFORM ANALYSIS OF STOKES-ANTI-STOKES STIMULATED RAMAN SCATTERING

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