Semiclassical solutions of the nonlinear Schrodinger equation

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.