On N-wave type systems and their gauge equivalent

Authors:
  • VGVladimir S. Gerdjikov
    Vladimir S. Gerdjikov
  • GGGeorgi G. Grahovski
    Georgi G. Grahovski
  • NKNikolay A. Kostov
    Nikolay 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 system L and related to some simple Lie algebra g are analyzed. Special attention is paid to the Z_2-reductions including ones that can be embedded also in the Weyl group of g. The consequences of these restrictions on the structure of the dresing factors are outlined. An example of 4-wave equations (with application to nonlinear optics) and its gauge equivalent are given.