Title screen

[References: p. 1465 (17 tit.)]

Quasi-energy states and a spectrum of quasi-energies asymptotic in small parameter h (h-0) are constructed for a multidimensional Hartree type equation with non-local nonlinearity and with an external field cyclic in time. The quasi-energy states are a special case of trajectory coherent solutions of the Hartree type equation, which belong to the class of semiclassically concentrated functions. A function of this class describes a solitary wave localized in a neighborhood of a phase trajectory in the space of moments of the solution. The phase trajectory is closed due to the configuration of the external field. The Aharonov-Anandan geometric phases, which characterize a system “as a whole”, are found for the quasi-energy states in a semiclassical approximation accurate to O(h3/2), h-0