Polynomial Lie algebra methods in solving the second-harmonic generation model: some exact and approximate calculations
V. P. Karassiov, A. A. Gusev, S. I. Vinitsky
Abstract
We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of a polynomial Lie algebra supd(2) and related spectral representations of the model evolution operator realized in algorithmic forms. It enabled us to implement computer experiments exhibiting a satisfactory accuracy of the cluster approximations in a large range of characteristic model parameters.
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