The evolution operator of the Hartree-type equation with a quadratic potential

Abstract

Based on the ideology of the Maslov's complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov-Anandan geometric phases are found in explicit form for the quasi-energy states.

23 peges

References in corpus (1)

• The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation

Cited by in corpus (4)

• Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation
• Semiclassical Propagation of Coherent States for the Hartree equation
• Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
• Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field