Двумерное уравнение типа Хартри: квазиклассические асимптотики и невязка

Abstract

The object of the article is solving of 2D Hartree type equation. We have used semiclassical approximation to pass from the nonlinear equation to analytically solvable equation. For Hartree type equation exact linear Hamilton equations and approximate equations for the second moments, based on semiclassical asymptotics, have been obtained. The exact expression for Green function has been obtained for approximate equation. So we have obtained analytical expression for the vast class of wave functions which are the approximate solution of nonlinear Hartree type equation. Computed function has specific behavior which reflects behavior of exact solution. Also we have obtained the error of the asymptotic solution to estimate its accuracy.