ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 35 Roman, Olena, Institute of Mathematics, Ukraine Symmetry of nonlinear equations of relativistical quantum mechanics We have studied symmetry properties of nonlinear equations for complex field. Nonlinear representations of the conformal algebra and the extended Poincare algebra are presented. Wide classes of the conformally invariant wave equations are constructed. Conditional symmetry of the nonlinear wave equation is studied. Part of these results is joint work with P. Basarab-Horwath and W. Fushchych. Reference: P. Basarab-Horwath, W. Fushchych, O. Roman, On a new conformal symmetry for a complex scalar field, Phys. Lett. A. 226 (1997), 150–154.