A concept of semiclassically concentrated solutions is formulated for the m
ultidimensional nonlinear Schrodinger equation (NLSE) with an external fiel
d. These solutions are considered as multidimensional solitary waves. The c
enter of mass of such a solution is shown to move along with the bicharacte
ristics of the basic symbol of the corresponding linear Schrodinger equatio
n. The leading term of the asymptotic WKB-solution is constructed for the m
ultidimensional NLSE. Special cases are considered for the standard one-dim
ensional NLSE and for NLSE in cylindrical coordinates.