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 -