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The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation

V. V. Belov·A. Yu. Trifonov·A. V. Shapovalov
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Abstract

The general construction of quasi-classically concentrated solutions to the Hartree-type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter \h (\h\to0), are constructed with a power accuracy of O(\h^{N/2}), where N is any natural number. In constructing the quasi-classically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for middle or centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of quasi-classically concentrated solutions of the Hartree-type equations. The results obtained are exemplified by the one-dimensional equation Hartree-type with a Gaussian potential.Comments: 6 pages, 4 figures, LaTeX Report no: Subj-class: Accelerator Physics

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V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov. 2000-12-28. The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation. https://doi.org/10.1155/s0161171202112142

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