Asymptotic perturbation theory applied to diffractive atomic scattering

1991 ◽  
Vol 8 (3) ◽  
pp. 509 ◽  
Author(s):  
J. Mizerski ◽  
W. Miklaszewski ◽  
S. Stenholm
Keyword(s):  
Perturbation Theory ◽  
Atomic Scattering ◽  
Asymptotic Perturbation

scholarly journals Degenerate asymptotic perturbation theory

1983 ◽  
Vol 90 (2) ◽  
pp. 219-233 ◽  
Author(s):  
W. Hunziker ◽  
C. A. Pillet
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Perturbation

scholarly journals Extrapolation of perturbation-theory expansions by self-similar approximants

2014 ◽  
Vol 25 (5) ◽  
pp. 595-628 ◽  
Author(s):  
S. GLUZMAN ◽  
V.I. YUKALOV
Keyword(s):  
Perturbation Theory ◽  
Approximation Theory ◽  
Asymptotic Expansions ◽  
Applied Mathematics ◽  
Self Similar ◽  
Similar Approximation ◽  
Asymptotic Perturbation

The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures.

Time asymptotic perturbation theory in weak plasma turbulence II. Vlasov description

1971 ◽  
Vol 5 (1) ◽  
pp. 39-49 ◽  
Author(s):  
Klaus Elsässer
Keyword(s):  
Perturbation Theory ◽  
Kinetic Equation ◽  
Mode Coupling ◽  
Asymptotic Methods ◽  
Resonant Mode ◽  
Landau Damping ◽  
The Poisson Equation ◽  
Hierarchy Equations ◽  
Coupling Terms ◽  
Asymptotic Perturbation

In electrostatic turbulence under appropriate conditions we show that we can have an equation for ϕk (time variation of electrostatic potential amplitude) which is essentially instantaneous in time. The coefficients in this equation are uniquely determined by the Poisson equation of the corresponding order. By applying time asymptotic methods of Bogoljubov and Mitropoiski to the corresponding hierarchy equations we obtain a kinetic equation for the spectrum 〈|ϕk|2〉. The resonant mode coupling terms agree with the usual ones. But the non-linear Landau damping terms, as given, e.g. by Frieman & Rutherford (1964), Kadomtsev (1965), Tsytovich (1968), and Rogister & Oberman (1969) are complemented by additional terms which are, at least formally, non-zero. For simplicity the calculations are only done for the weakly unstable (and weakly damped) modes.

Sign in / Sign up

Export Citation Format

Share Document