Semiclassical trajectory-coherent approximations of Hartree-type equations

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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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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