Vladimir GERDJIKOV
Institute for Nuclear Research and Nuclear Energy,
Bulgarian Academy of Sciences,
72 Tsarigradsko chaussee,
1784 Sofia, BULGARIA

Nikolay KOSTOV
Institute of Electronics,
Bulgarian Academy of Sciences,
72 Tsarigradsko chaussee,
1784 Sofia, BULGARIA
E-mail: nakostov@ie.bas.bg
 

On N-wave type systems and their gauge equivalent

Abstract:
The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra g are derived and analyzed. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. The Z₂-reductions including ones that can be embedded also in the Weyl group of g. The hierarchy of the Hamiltonian structures to the gauge equivalent systems to the N-wave ones is also discussed.