Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark

Reductions in integrable systems. Reduction group. Dihedral group of an arbitrary order as a reduction group
by Sergey Senchenko
Upsala University

Thursday December 7, 2000, 14.30 h
at MIDIT, IMM, Bldg. 305, Room 027, DTU,

Abstract: In this paper I have considered the certain class of nonlinear equations. All investigated equations are integrable by means of inverse scattering method. The equivalence relation with respect to the action of finite groups is imposed. Dihedral groups of an arbitrary order were used as a reduction groups. Finally the whole set of nonlinear equations had been divided into the finite number of types. The equations of each type depend upon one parameter-the order of relevant reduction group. This classification is complete, i.e. it comprises all equations of considered type and accounts all dihedral groups.