ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 35 Alexander A Alexeyev, Laboratory of Computer Physics and Mathematical Simulation, Peoples’ Friendship University, Moscow, Russia Superposition principles for nonlinear partial differential equations in (1+1) dimension An approach similar to a superposition principle for ODEs is proposed for NPDEs in (1+1) dimension. Such equations associated with truncated Painleve expansions are considered, and the possibility of permutability for the simplest solitary waves and another solution with suitable boundary conditions is shown. The latter before and after an collision can be connected vie a nonparametric transformation in view of its evolution without other perturbations. In the simplest case, the above just results in a phase shift. The MKdV, Burgers, Sawada-Kotera, etc cases were investigated, and two-soliton solutions were constructed. Reference: A A Alexeyev, A superposition principle for NPDEs, in preparation (1998).