Semiclassical trajectory-coherent states of the nonlinear Schrödinger equation with unitary nonlinearity

O. V. Zhdaneev, G. N. Sheehan, A. Yu Trifonov, Aleksandr Vasilievich Shapovalov

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Abstract

Semiclassically concentrated states of the nonlinear Schrödinger equation (NLSE) with unitary nonlinearity, representing multidimensional localized wave packets, are constructed on the basis of the Maslov complex germ theory. A system of ordinary differential equations of Hamilton-Ehrenfest (HE) type, describing the motion of the wave packet centroid, is derived. The structure of the HE system is strongly influenced by the initial conditions of the Cauchy problem for the NLSE. Wave packets of Gaussian type are constructed in an explicit form. Possible use of the solutions constructed in the problem of optical pulse propagation in a nonlinear medium with nonstationary dispersion is discussed.

Original languageEnglish
Pages (from-to)598-606
Number of pages9
JournalRussian Physics Journal
Volume42
Issue number7
DOIs
Publication statusPublished - 1 Jan 1999

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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