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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Green's function
Green's functions
operators
Symmetry
Cauchy problem
Evolution Operator
symmetry
Operator
Cauchy Problem
Exact Solution
Class
Family

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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title = "Green's function of a hartree-type equation with a quadratic potential",
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.",
keywords = "Hartree-type equation, Maslov complex germ method, symmetry operators",
author = "Lisok, {Alexander Leonidovich} and Trifonov, {A. Yu} and Shapovalov, {Aleksandr Vasilievich}",
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AU - Lisok, Alexander Leonidovich

AU - Trifonov, A. Yu

AU - Shapovalov, Aleksandr Vasilievich

PY - 2004/11/1

Y1 - 2004/11/1

N2 - 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.

AB - 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.

KW - Hartree-type equation

KW - Maslov complex germ method

KW - symmetry operators

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