Theoretical Physics Department, Tomsk State University
36, Lenin ave. 634050 Tomsk, RUSSIA
E-mail: shpv@phys.tsu.ru
 

Semiclassically concentrated waves for the generalized nonlinear Schrodinger equation with external field
by A.V. Shapovalov and A. Yu. Trifonov

Abstract:
A class of semiclassically concentrated solutions (SCS), asymptotic in a small parameter  h, h --> 0, is constructed in the
frame of the WKB--Maslov method to the qubic nonlinear Schrodinger equation (NSE) in a multidimensional space with an
external field. The dynamics of the one-dimensional NSE-soliton in an external field of a special form is discussed. Asymptotic
expressions are found for the parameters of the soliton in the external field.
The non-local generalization of the NSE, the Hatree type equation (HTE), is considered in terms of the complex WKB--Maslov method. The general construction of the SCS to the HTE is presented. The SCS construction is based on solution of a dynamic system (the Hamilton--Ehrenfest system) and on a linear Schrodinger equation (the associated Schrodinger equation).  The nonlinear superposition principle is formulated for the SCS of the HTE. An example of the one-dimensional HTE is considered.

The work was supported in part by the Russian Foundation for Basic Research (Grant No. 00-01-00087) and the Ministry of Education of the Russian Federation (Grant No. E 00-1.0-126).