Classical and Quantum Mechanical (QM) Effects in the One-Soliton   solution of the EM Nonlinear Schrodinger (NLS) Equation
  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. 
Y. Ben-Aryeh
quant-ph