钟摆型方程绝热极限的类wkb方法

International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450) Pub Date : 1900-01-01 DOI:10.1109/DD.2000.902355

Andrey V. Ivanov

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引用次数: 0

摘要

我们考虑二阶x/spl uml/+/spl psi/(/spl epsi/t) sin(x-/spl phi/(/spl epsi/t))=0的常微分方程，系数/spl psi/和/spl phi/随时间缓慢变化。利用WKB类方法构造了方程在极限/spl epsi//spl rarr/0(绝热极限)下的通解的两个渐近级数。其中一个在变量t远离系数/spl /时成立另一个在这些0的邻域内成立。

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

We consider the ordinary differential equation of the second order x/spl uml/+/spl psi/(/spl epsi/t) sin(x-/spl phi/(/spl epsi/t))=0 with the coefficients /spl psi/ and /spl phi/ 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 /spl epsi//spl rarr/0 (adiabatic limit). One of them is true when the variable t is far from the zeroes of the coefficient /spl psi/ and the other one is valid in the neighborhoods of these these zeroes.

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来源期刊

$International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450)$

International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450)

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