Результаты поиска по 'semiclassical approximation':
Найдено статей: 4
  1. Levchenko E.A., Trifonov A.Y., Shapovalov A.V.
    Semiclassical approximation for the nonlocal multidimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation
    Computer Research and Modeling, 2015, v. 7, no. 2, pp. 205-219

    Semiclassical asymptotic solutions with accuracy $O(D^{N/2})$, $N\geqslant3$ are constructed for the multidimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation in the class of trajectory-concentrated functions. Using the symmetry operators a countable set of asymptotic solutions with accuracy $O(D^{3/2})$ is obtained. Asymptotic solutions of two-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation are found in explicit
    form.

    Keywords: nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation, asymptotic solution, Einstein— Ehrenfest system.
    Views (last year): 4.
  2. Borisov A.V., Trifonov A.Y., Shapovalov A.V.
    Semiclassical solutions localized in a neighborhood of a circle for the Gross–Pitaevskii equation
    Computer Research and Modeling, 2009, v. 1, no. 4, pp. 359-365

    Non-collapsing soliton-like wave functions are shown to exist in semiclassical approximation for the Bose-Einstein condensate model based on the Gross–Pitaevskii equation with attractive nonlinearity and external field of magnetic trap of special form.

    Keywords: Gross–Pitaevskii equation, Bose–Einstein condensate, magneto-optical trap.
    Citations: 1 (RSCI).
  3. Rezaev R.O., Trifonov A.Y., Shapovalov A.V.
    The Einstein−Ehrenfest system of (0, M)-type and asymptotical solutions of the multidimensional nonlinear Fokker−Planck−Kolmogorov equation
    Computer Research and Modeling, 2010, v. 2, no. 2, pp. 151-160

    Semiclassical approximation formalism is developed for the multidimensional Fokker–Planck–Kolmogorov equation with non-local and nonlinear drift vector with respect to a small diffusion coefficient D, D→0, in the class of trajectory concentrated functions. The Einstein−Ehrenfest system of (0, M)-type is obtained. A family of semiclassical solutions localized around a point driven by the Einstein−Ehrenfest system accurate to O(D(M+1)/2) is found.

    Keywords: nonlinear Fokker−Planck−Kolmogorov equation, semiclassical asymptotics, WKB-Maslov method, Einstein−Ehrenfest system.
    Views (last year): 2.
  4. Trifonov A.Y., Masalova E.A., Shapovalov A.V.
    Semiclassical asymptotics of nonlinear Fokker–Plank equation for distributions of asset returns
    Computer Research and Modeling, 2009, v. 1, no. 1, pp. 41-49

    The semiclassical approximation method is applied for solution construction of the Fokker–Planck equation with quadratic nonlocal nonlinearity and various coefficients in models of asset returns estimation. Analitical expressions determining nonlinear evolution operator are obtained in semiclasical approximation.

    Keywords: Fokker–Plank equation, semiclassical approximation, economics.
    Citations: 1 (RSCI).

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