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.

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U2 - 10.1023/A:1014719007121

DO - 10.1023/A:1014719007121

M3 - Article

AN - SCOPUS:0036243766

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 -