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Polynomial Lie algebra methods in solving the second-harmonic generation model: some exact and approximate calculations. (English) Zbl 1039.81525

Summary: 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 su\(_{pd}(2)\) 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.

MSC:

81R05 Finite-dimensional groups and algebras motivated by physics and their representations

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