  The complex WKB-Maslov method is used to consider an approach to the
semiclassical integrability of the multidimensional Gross-Pitaevskii equation
with an external field and nonlocal nonlinearity previously developed by the
authors. Although the WKB-Maslov method is approximate in essence, it leads to
exact solution of the Gross-Pitaevskii equation with an external and a nonlocal
quadratic potential. For this equation, an exact solution of the Cauchy problem
is constructed in the class of trajectory concentrated functions. A nonlinear
evolution operator is found in explicit form and symmetry operators (mapping a
solution of the equation into another solution) are obtained for the equation
under consideration. General constructions are illustrated by examples.
