Title :
WKB-like method for the adiabatic limit of a pendulum type equation
Author_Institution :
Dept. of Math. Phys., St. Petersburg State Univ.
Abstract :
We consider the ordinary differential equation of the second order x¨+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 :
WKB calculations; nonlinear differential equations; series (mathematics); WKB-like method; Wentzel-Kramers-Brillouin-like method; adiabatic limit; asymptotic series; general solution; ordinary differential equation; pendulum type equation; Differential equations; Diffraction; Jacobian matrices; Nonlinear equations; Physics; Turning;
Conference_Titel :
Day on Diffraction Millenniuym Workshop, 2000. International Seminar
Conference_Location :
St. Petersburg
Print_ISBN :
5-7997-0252-4
DOI :
10.1109/DD.2000.902355
