Statistical Modelling of Propagation and Interaction of Solitons in Fiber-Optic Lines

AUTHOR(S):

TITLE

Statistical Modelling of Propagation and Interaction of Solitons in Fiber-Optic Lines

ABSTRACT

The paper presents a constructive way to modell the soliton propagate described by the classical nonlinear Schrodinger equation. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. We consider the features of statistical calculations requiring large computational resources on BFNT stage of NIS method. We investigate numerically the feasibility of merging the NIS technique in a burst mode with high spectral efficiency methods showing a performance improvement.

KEYWORDS

Statistical modelling, Monte Carlo methods, SDE, nonlinear Schrodinger equation, solitons, optical fiber

REFERENCES

[1] G. Agrawal, Nonlinear fiber optics, Academic Press, New York , 1996

[2] S.T. Lee, J.E. Prilepsky, S.,K. Turitsyn, Non- linear inverse synthesis for high spectral effi- ciency transmission in optical fibers. OPTICS EXPRESS, Vol. 22, No 22 , 2014.

[3] V. E. Zakharov and A. B. Shabat, Exact the- ory of two-dimensional self-focusing and one- dimensional selfmodulation of waves in nonlin- ear media, Sov. Phys. JETP 34, 6269 , 1972.

[4] M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, The inverse scattering transform-Fourier analysis for nonlinear problems, Stud. Appl. Math. 53, 249315, 1974.

[5] V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons. The In- verse Scattering Method. Colsultants Bureau, New York, , 1984.

[6] M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform. SIAM, Philadel- phia, 1981.

[7] A. C. Newell, Solitons in mathematics and physics. SIAM, Philadelphia, 1985.

[8] G. Boffetta and A. R. Osborne, Computation of the direct scattering transform for the nonlinear Schroedinger equation, J. Comput. Phys. 102(2), 252264, 1992.

[9] O. V. Belai, L. L. Frumin, E. V. Podivilov, and D. A. Shapiro, Efficient numerical method of the fiber Bragg grating synthesis, J. Opt. Soc. Am. B 24(7), 14511457, 2007.

[10] T.A. Averina and S.S Artemiev, Analysis of Accuracy of Monte Carlo Methods in Solving Boundary Value Problems by Probabilistic Rep- resentations, Sib. Zh. Vych. Mat., (2008) , vol. 11, no. 3, pp. 239-250.

Cite this paper

Vitaliy Lukinov. (2017) Statistical Modelling of Propagation and Interaction of Solitons in Fiber-Optic Lines. International Journal of Mathematical and Computational Methods, 2, 366-371