Abstract
We analytically and numerically investigate the solution to the stationary Gross-Pitaevskii equation for a one-dimensional potential of the optical lattice in the case of repulsive nonlinearity. From the mathematical viewpoint, this problem is similar to the well-known problem of the classical mathematical Kapitza pendulum perturbed by a weak high-frequency force. At certain values of the parameters, dynamic chaos is produced in the considered problem. It is modeled analytically by a nonlinear diffusion equation.
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Original Russian Text © H.A. Ishkhanyan, V.P. Krainov, 2011, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2011, Vol. 140, No. 3, pp. 466–471.
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Ishkhanyan, H.A., Krainov, V.P. Dynamic chaos in the solution of the Gross-Pitaevskii equation for a periodic potential. J. Exp. Theor. Phys. 113, 407–411 (2011). https://doi.org/10.1134/S1063776111070028
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DOI: https://doi.org/10.1134/S1063776111070028