### 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 language | English |
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Pages (from-to) | 1528-1541 |

Number of pages | 14 |

Journal | Theoretical and Mathematical Physics |

Volume | 141 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Nov 2004 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Green's function of a hartree-type equation with a quadratic potential.** / Lisok, Alexander Leonidovich; Trifonov, A. Yu; Shapovalov, Aleksandr Vasilievich.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Green's function of a hartree-type equation with a quadratic potential

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

UR - http://www.scopus.com/inward/record.url?scp=8144227575&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=8144227575&partnerID=8YFLogxK

U2 - 10.1023/B:TAMP.0000046561.88206.f9

DO - 10.1023/B:TAMP.0000046561.88206.f9

M3 - Article

VL - 141

SP - 1528

EP - 1541

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 2

ER -