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
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.