H. Landa, M. Drewsen, B. Reznik, A. Retzker
We propose an expansion of the solutions of linearly coupled Mathieu equations in terms of infinite continued matrix inversions, and use it to find the modes which diagonalize the dynamical problem. This allows to obtain explicitly the ('Floquet-Lyapunov') transformation to coordinates in which the motion is that of decoupled linear oscillators. We use this transformation to find the corresponding quantum wavefunctions for stable oscillations. The expansion is not perturbative and can be applied to more general linear systems with periodic coefficients (coupled Hill equations), and to nonlinear systems as a starting point for convenient perturbative treatment of the nonlinearity.
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http://arxiv.org/abs/1206.0716
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