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Conference publicationsSemiclassical approximation for the nonlinear Schroedinger equation with external fieldRussia, Tomsk Ideas of the complex germ theory are used to construct analytical solutions, asymptotic in a small parameter h, h→0, for the multidimensional nonlinear Schrodinger equation (NLSE) with an external field and local cubic nonlinearity. The asymptotics are looked for in a class of functions concentrated in a neighborhood of an unclosed surface associated with a phase curve that describes evolution of the surface vertex. Functions of the class have the NLSE - one-soliton form in the direction of the surface normal. A semiclassical linearization is realized for the NLSE to O(h3/2), h→0, and a linear associated Schrodinger equation is obtained. |
