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[1] Belinskii A. V., Chirkin A. S. Quantum-theory of nonlinear propagation of schrodinger solitons - squeezed states and sub-poisson statistics // Journal of Experimental and Theoretical Physics. — 1990. — Vol. 71, no. 2. — P. 228–233. A quantum theory of propagation of solitons in a nonlinear medium is developed based on the nonlinear Schrodinger equation for the operators of the positive- and negative-frequency parts of the field. A derivation of this equation is given in the functional integration representation, which is convenient for the analysis of the dynamics of quantum field fluctuations. The propagation of a fundamental soliton, initially in a coherent state, is analyzed. It is shown that the statistics of the soliton photons in the nonlinear medium does not change. At the same time the fluctuations of one of the quadrature components of the field may be suppressed under certain conditions. Interference between the soliton and the coherent radiation alters the photon statistics of the resulting field. The conditions under which optimal suppression of the fluctuations of the number of photons is ensured and their sub-Poisson statistics is reached are elucidated and analyzed.

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