ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 33,34 Nakano, Minoru, KEIO University On the WKB method and Airy functions. We consider double asymptotic property of WKB solutions of

(∗)  ε^{3}y′′′ − 4εxy′ − 2y = 0 (|x| ≤ x_{0}, 0 < ε ≤ ε_{0}).

When ε = 1, solutions of (∗) are given by products of the Airy functions: Ai^{2}(x), Ai(x)Bi(x), Bi^{2}(x). We analyze relation between WKB solutions of (∗) and Airy functions. References

[1] Fedoryuk. Asymptotic analysis. Springer Verlag.

[2] Nakano. On products of the Airy functions and the WKB method. J. Tech. Univ. Plovdiv. 1 (1995) 27-38

[3] Zwillinger. Handbook of Diff. Eqs. Academic Press.