  Propagation effects are analyzed for electromagnetic (EM) waves which satisfy
the one-soliton non-linear Schrodinger (NLS) equation in a dispersive wave
guide. The coupling between momentum and frequencies due to dispersion relation
is treated by a coupled Hamiltonian-Momentum operator with equal-space
commutation relations(CR). Kerr interactions in the soliton are treated. The
classical solution of the one-soliton with possible quantum effects are
analyzed. The integrability of nonlinear equations is related to
compatibility-condition for scattering matrices and such relation is applied to
the NLS equation.
