Conference publications

Semiclassical approximation for the nonlinear Schroedinger equation with external field

Borisov A. V., Trifonov A. Yu., Shapovalov A. V.

Russia, Tomsk

"Математика. Компьютер. Образование". Cб. трудов XII международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2005. Vol. 2, 466pp. Pp. 648-659.

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.

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