The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation
Belov, V. V. ; Trifonov, A. Yu. ; Shapovalov, A. V.
arXiv, 0012046 / Harvested from arXiv
Text on arXiv
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
Publié le : 2000-12-28
Classification:  Mathematical Physics 
@article{0012046,
     author = {Belov, V. V. and Trifonov, A. Yu. and Shapovalov, A. V.},
     title = {The Trajectory-Coherent Approximation and the System of Moments for the
  Hartree-Type Equation},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0012046}
}

Belov, V. V.; Trifonov, A. Yu.; Shapovalov, A. V. The Trajectory-Coherent Approximation and the System of Moments for the
  Hartree-Type Equation. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0012046/