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26 April 2024 |
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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
; | | Date: |
28 Dec 2000 | | Subject: | Mathematical Physics | math-ph math.MP | | Affiliation: | Moscow Institute of Electronics and Mathematics), A.Yu. Trifonov(Tomsk Polytechnic University) and A.V. Shapovalov(Tomsk State University | | 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 o0), 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 | | Source: | arXiv, math-ph/0012046 | | Services: | Forum | Review | PDF | Favorites | |
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