ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

16. Applications

1991 MS Classification: 35 Abramochkin, Eugeny, Physics Institute, Samara, Russia Structurally stable singular wavefields Laguerre-Gaussian functions are well-known solutions of 2D harmonic oscillator equation. The modulus structure of a LG function that has the only zero of order m is simple: it looks like a light ring (or a light spot in case m = 0) on the black background. A generalization of these functions is proposed, namely, for any closed curve on the plane there exists a function family depending on a pair of integer-valued parameters, any member of which is structurally stable solution of the Schrodinger equation. In particular, when the curve is a circumference the whole set of LG functions is obtained.