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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.

preprint2011arXivOpen access
Y. Ben-Aryeh
quant-ph
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Y. Ben-Aryeh

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