Green's function of a hartree-type equation with a quadratic potential

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Abstract

Using the complex WKB-Maslov method, we consider a solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically supported functions. In this class, we obtain the evolution operator explicitly. We find parametric families of symmetry operators of the Hartree-type equation. Using the symmetry operators, we construct a family of exact solutions of this equation.

Original languageEnglish
Pages (from-to)1528-1541
Number of pages14
JournalTheoretical and Mathematical Physics
Volume141
Issue number2
DOIs
Publication statusPublished - 1 Nov 2004

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Keywords

  • Hartree-type equation
  • Maslov complex germ method
  • symmetry operators

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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