Second Order Reductions of $N$-Wave Interactions Related to Low-rank Simple Lie Algebras

Gerdjikov, Vladimir; Grahovski, Georgi; Kostov, Nikolay

doi:10.7546/giq-1-2000-55-77

VOL. 1 | 2000 Second Order Reductions of $N$-Wave Interactions Related to Low-rank Simple Lie Algebras

Chapter Author(s) Vladimir Gerdjikov, Georgi Grahovski, Nikolay Kostov

Editor(s) Ivaïlo M. Mladenov, Gregory L. Naber

Geom. Integrability & Quantization, 2000: 55-77 (2000) DOI: 10.7546/giq-1-2000-55-77

Abstract

The analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method (ISM) is interesting and still an open problem. We show how the second-order reductions of the $N$-wave interactions related to low-rank simple Lie algebras can be embedded in the Weyl group of $\mathfrak{g}$. Some of the reduced systems find applications to nonlinear optics