Asymptotic Perturbation Theory of Waves

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.

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Asymptotic perturbation theory applied to diffractive atomic scattering

Journal of the Optical Society of America B ◽

10.1364/josab.8.000509 ◽

1991 ◽

Vol 8 (3) ◽

pp. 509 ◽

Cited By ~ 7

Author(s):

J. Mizerski ◽

W. Miklaszewski ◽

S. Stenholm

Keyword(s):

Perturbation Theory ◽

Atomic Scattering ◽

Asymptotic Perturbation

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

Journal of Plasma Physics ◽

10.1017/s0022377800005535 ◽

1971 ◽

Vol 5 (1) ◽

pp. 39-49 ◽

Cited By ~ 7

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.

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