The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation
Abstract
The general construction of quasi-classically 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 \h (\h\to0), are constructed with a power accuracy of O(\h^{N/2}), where N is any natural number. In constructing the quasi-classically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for middle or centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of quasi-classically concentrated solutions of the Hartree-type equations. The results obtained are exemplified by the one-dimensional equation Hartree-type with a Gaussian potential.Comments: 6 pages, 4 figures, LaTeX Report no: Subj-class: Accelerator Physics
Keywords
Cite
@article{arxiv.math-ph/0012046,
title = {The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation},
author = {V. V. Belov and A. Yu. Trifonov and A. V. Shapovalov},
journal= {arXiv preprint arXiv:math-ph/0012046},
year = {2016}
}
Comments
36 pages, LaTeX-2e