Лукинов В.Л.  

Solving the nonlinear Schrödinger equation by Monte Carlo method

The work is devoted to the numerical analysis of solution of the nonlinear Schrödinger equation with additive Gaussian noise, describing the propagation of light pulses in fiber-optic communication lines (FOL) [1]. The spectral efficiency of fiber-optic soliton, as well as the effects that affect its growth is investigated. With the combination of a non-linear analogue of the Fourier method of splitting into physical processes in the long sections [2, 3], and Euler's method for the solution of a short section of the SDE [4] a stochastic analysis of the interaction of two solitons is conducted. Statistical modeling on supercomputer helps us to study the stability of solitons over long distances, depending on the characteristics of random noise transmitter and noise generated because of an optically amplified spontaneous emission.
The project has been partially supported by grants of RFBR (projects 14-01-00340 and 14-01-31451). 

1. G. A. Agrawal, Nonlinear Fiber Optic, Academic Press, Boston, 2001.  
2. A. A. Redyuk, A. S. Skidin, A. V. Shafarenko, M. P. Fedoruk, “Direct modelling of error statistics for data transmission through a high data rate communication line using a four-level phase modulation format”, Kvant. electron., 42:7 (2012), 645–649
3. A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre”, Kvant. electron., 39:8 (2009), 765–769
4. Artemiev S.S. etc., The analysis of stochastic fluctuations by Monte Carlo method on supercomputers, Novosibirsk, 2015 (in print)

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