The trajectory-coherent approximation and the system of moments for the hartree type equation

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Abstract

The general construction of semiclassically 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 □ (□→0), are constructed with a power accuracy of O (□ N/2), where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.

Original languageEnglish
Pages (from-to)325-370
Number of pages46
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume32
Issue number6
DOIs
Publication statusPublished - 1 Jan 2002

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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