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WKB-like method for the adiabatic limit of a pendulum type equation. / Ivanov, A. V.

International Seminar Day on Diffraction Millennium Workshop, DD 2000 - Proceedings. 2000. p. 40-46.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Ivanov, AV 2000, WKB-like method for the adiabatic limit of a pendulum type equation. in International Seminar Day on Diffraction Millennium Workshop, DD 2000 - Proceedings. pp. 40-46. https://doi.org/10.1109/DD.2000.902355

APA

Ivanov, A. V. (2000). WKB-like method for the adiabatic limit of a pendulum type equation. In International Seminar Day on Diffraction Millennium Workshop, DD 2000 - Proceedings (pp. 40-46) https://doi.org/10.1109/DD.2000.902355

Vancouver

Ivanov AV. WKB-like method for the adiabatic limit of a pendulum type equation. In International Seminar Day on Diffraction Millennium Workshop, DD 2000 - Proceedings. 2000. p. 40-46 https://doi.org/10.1109/DD.2000.902355

Author

Ivanov, A. V. / WKB-like method for the adiabatic limit of a pendulum type equation. International Seminar Day on Diffraction Millennium Workshop, DD 2000 - Proceedings. 2000. pp. 40-46

BibTeX

@inproceedings{00e424de9f6640d499069a2c147773bf,
title = "WKB-like method for the adiabatic limit of a pendulum type equation",
abstract = "We consider the ordinary differential equation of the second order ẍ+ψ(εt) sin(x-φ(εt))=0 with the coefficients ψ and φ depending slowly on time. By using a Wentzel-Kramers-Brillouin (WKB)-like method we construct two asymptotic series for a general solution of the equation in the limit ε→0 (adiabatic limit). One of them is true when the variable t is far from the zeroes of the coefficient ψ and the other one is valid in the neighborhoods of these these zeroes.",
keywords = "Differential equations, Diffraction, Jacobian matrices, Nonlinear equations, Physics, Turning",
author = "Ivanov, {A. V.}",
year = "2000",
month = jan,
day = "1",
doi = "10.1109/DD.2000.902355",
language = "English",
pages = "40--46",
booktitle = "International Seminar Day on Diffraction Millennium Workshop, DD 2000 - Proceedings",

}

RIS

TY - GEN

T1 - WKB-like method for the adiabatic limit of a pendulum type equation

AU - Ivanov, A. V.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - We consider the ordinary differential equation of the second order ẍ+ψ(εt) sin(x-φ(εt))=0 with the coefficients ψ and φ depending slowly on time. By using a Wentzel-Kramers-Brillouin (WKB)-like method we construct two asymptotic series for a general solution of the equation in the limit ε→0 (adiabatic limit). One of them is true when the variable t is far from the zeroes of the coefficient ψ and the other one is valid in the neighborhoods of these these zeroes.

AB - We consider the ordinary differential equation of the second order ẍ+ψ(εt) sin(x-φ(εt))=0 with the coefficients ψ and φ depending slowly on time. By using a Wentzel-Kramers-Brillouin (WKB)-like method we construct two asymptotic series for a general solution of the equation in the limit ε→0 (adiabatic limit). One of them is true when the variable t is far from the zeroes of the coefficient ψ and the other one is valid in the neighborhoods of these these zeroes.

KW - Differential equations

KW - Diffraction

KW - Jacobian matrices

KW - Nonlinear equations

KW - Physics

KW - Turning

UR - http://www.scopus.com/inward/record.url?scp=84983194005&partnerID=8YFLogxK

U2 - 10.1109/DD.2000.902355

DO - 10.1109/DD.2000.902355

M3 - Conference contribution

AN - SCOPUS:84983194005

SP - 40

EP - 46

BT - International Seminar Day on Diffraction Millennium Workshop, DD 2000 - Proceedings

ER -

ID: 95584726