Semiclassical trajectory-coherent approximations of Hartree-type equations

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12 Citations (Scopus)

Abstract

We use the concept of the complex WKB-Maslov method to construct semiclassically concentrated solutions for Hartree-type equations. Formal solutions of the Cauchy problem for this equation that are asymptotic (with respect to a small parameter ℏ, ℏ → 0) are constructed with the power-law accuracy O(ℏN/2), where N ≥ 3 is a positive integer. The system of Hamilton-Ehrenfest equations (for averaged and centered moments) derived in this paper plays a significant role in constructing semiclassically concentrated solutions. In the class of semiclassically concentrated solutions of Hartree-type equations, we construct an approximate Green's function and state a nonlinear superposition principle.

Original languageEnglish
Pages (from-to)391-418
Number of pages28
JournalTheoretical and Mathematical Physics
Volume130
Issue number3
DOIs
Publication statusPublished - 1 Dec 2002

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trajectories
Trajectory
Approximation
approximation
Formal Solutions
Cauchy problem
Small Parameter
Superposition
integers
Green's function
Cauchy Problem
Power Law
Green's functions
Moment
moments
Integer
Concepts
Class

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Semiclassical trajectory-coherent approximations of Hartree-type equations. / Belov, V. V.; Trifonov, A. Yu; Shapovalov, Aleksandr Vasilievich.

In: Theoretical and Mathematical Physics, Vol. 130, No. 3, 01.12.2002, p. 391-418.

Research output: Contribution to journalArticle

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