Abstract
The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter □ (□→0), are constructed with a power accuracy of O (□ N/2), where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.
| Original language | English |
|---|---|
| Pages (from-to) | 325-370 |
| Number of pages | 46 |
| Journal | International Journal of Mathematics and Mathematical Sciences |
| Volume | 32 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Jan 2002 |
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ASJC Scopus subject areas
- Mathematics (miscellaneous)
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The trajectory-coherent approximation and the system of moments for the hartree type equation. / Belov, V. V.; Trifonov, A. Y U; Shapovalov, Aleksandr Vasilievich.
In: International Journal of Mathematics and Mathematical Sciences, Vol. 32, No. 6, 01.01.2002, p. 325-370.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The trajectory-coherent approximation and the system of moments for the hartree type equation
AU - Belov, V. V.
AU - Trifonov, A. Y U
AU - Shapovalov, Aleksandr Vasilievich
PY - 2002/1/1
Y1 - 2002/1/1
N2 - The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter □ (□→0), are constructed with a power accuracy of O (□ N/2), where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.
AB - The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter □ (□→0), are constructed with a power accuracy of O (□ N/2), where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.
UR - http://www.scopus.com/inward/record.url?scp=2442451497&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=2442451497&partnerID=8YFLogxK
U2 - 10.1155/S0161171202112142
DO - 10.1155/S0161171202112142
M3 - Article
VL - 32
SP - 325
EP - 370
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
SN - 0161-1712
IS - 6
ER -