Geodesic
Green's Function of a Hartree-Type Equation with a Quadratic Potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 2, pp. 228-242 Cet article a éte moissonné depuis la source Math-Net.Ru

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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: Maslov complex germ method, Hartree-type equation, symmetry operators. 
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A. L. Lisok; A. Yu. Trifonov; A. V. Shapovalov. Green's Function of a Hartree-Type Equation with a Quadratic Potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 2, pp. 228-242. http://geodesic.mathdoc.fr/item/TMF_2004_141_2_a4/

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