Abstract
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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