Abstract
The method of semi-classical asymptotics is applied to a many-dimensional nonlinear Schrodinger equation with an external anisotropic oscillator field. Solutions asymptotic in a small parameter ħ, ħ → 0, are constructed in the class of functions localized in the neighborhood of an unclosed parabolic surface associated with the phase curve that describes the evolution of the vertex of this surface. In the normal direction to the surface, the functions have the form of the one-soliton solution of a one-dimensional nonlinear Schrodinger equation. The asymptotic evolution operator is considered accurate to O(ħ3/2), ħ → 0, in the specified class of solutions. The phenomenon of collapse is discussed.
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