
Symmetry in Nonlinear Mathematical Physics  2009
Harold Blas (Instituto de FísicaUFMT, Brasil)
NLS bright and dark solitons in the dressing transformation and tau function approach
Abstract:
We discuss some aspects of a generalized nonlinear Schrödinger
equation (GNLS). This system is associated to sl(n) affine KacMoody
algebra through a zerocurvature formulation. Using the dressing
transformation method we construct the Nsoliton solutions. As a
reduced submodel we obtain the socalled coupled nonlinear
Schrödinger equation (CNLS), which has been recently considered in
many physical applications. The both vanishing and nonvanishing
boundary conditions are considered, which give rise to the bright
and dark solitons, respectively. The explicit computations of some
matrix elements using the highest weight and the level one vertex
operator representations are outlined.

