The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation

Details The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation

2000-12-28

arxiv.org/abs/math-ph/0012046v1

Int. J. Math. and Math. Scien. (2002), Vol 32, N 6, P. 325-370

Physics

Mathematical Physics

36 pages, LaTeX-2e

Scientific paper

10.1155/S0161171202112142

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

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