Abstract
We use the concept of the complex WKB-Maslov method to construct semiclassically concentrated solutions for Hartree-type equations. Formal solutions of the Cauchy problem for this equation that are asymptotic (with respect to a small parameter ℏ, ℏ → 0) are constructed with the power-law accuracy O(ℏN/2), where N ≥ 3 is a positive integer. The system of Hamilton-Ehrenfest equations (for averaged and centered moments) derived in this paper plays a significant role in constructing semiclassically concentrated solutions. In the class of semiclassically concentrated solutions of Hartree-type equations, we construct an approximate Green's function and state a nonlinear superposition principle.
| Original language | English |
|---|---|
| Pages (from-to) | 391-418 |
| Number of pages | 28 |
| Journal | Theoretical and Mathematical Physics |
| Volume | 130 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Dec 2002 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Semiclassical trajectory-coherent approximations of Hartree-type equations. / Belov, V. V.; Trifonov, A. Yu; Shapovalov, Aleksandr Vasilievich.
In: Theoretical and Mathematical Physics, Vol. 130, No. 3, 01.12.2002, p. 391-418.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Semiclassical trajectory-coherent approximations of Hartree-type equations
AU - Belov, V. V.
AU - Trifonov, A. Yu
AU - Shapovalov, Aleksandr Vasilievich
PY - 2002/12/1
Y1 - 2002/12/1
N2 - We use the concept of the complex WKB-Maslov method to construct semiclassically concentrated solutions for Hartree-type equations. Formal solutions of the Cauchy problem for this equation that are asymptotic (with respect to a small parameter ℏ, ℏ → 0) are constructed with the power-law accuracy O(ℏN/2), where N ≥ 3 is a positive integer. The system of Hamilton-Ehrenfest equations (for averaged and centered moments) derived in this paper plays a significant role in constructing semiclassically concentrated solutions. In the class of semiclassically concentrated solutions of Hartree-type equations, we construct an approximate Green's function and state a nonlinear superposition principle.
AB - We use the concept of the complex WKB-Maslov method to construct semiclassically concentrated solutions for Hartree-type equations. Formal solutions of the Cauchy problem for this equation that are asymptotic (with respect to a small parameter ℏ, ℏ → 0) are constructed with the power-law accuracy O(ℏN/2), where N ≥ 3 is a positive integer. The system of Hamilton-Ehrenfest equations (for averaged and centered moments) derived in this paper plays a significant role in constructing semiclassically concentrated solutions. In the class of semiclassically concentrated solutions of Hartree-type equations, we construct an approximate Green's function and state a nonlinear superposition principle.
UR - http://www.scopus.com/inward/record.url?scp=0036243766&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036243766&partnerID=8YFLogxK
U2 - 10.1023/A:1014719007121
DO - 10.1023/A:1014719007121
M3 - Article
VL - 130
SP - 391
EP - 418
JO - Theoretical and Mathematical Physics(Russian Federation)
JF - Theoretical and Mathematical Physics(Russian Federation)
SN - 0040-5779
IS - 3
ER -