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


by Robert M. Miura
Department of Mathematics,
University of British Columbia
Vancouver, B.C.

MIDIT-seminar 458

Thursday July 15, 1999, 15.00 h
at MIDIT, IMM Building 305, room 027

Abstract: In the 1840s, John Scott Russell observed and studied a solitary surface water wave which he called the "great wave of translation." In 1895, Korteweg and de Vries (KdV) derived their equation that describes these solitary waves. Seventy years later, in 1965, Kruskal and Zabusky discovered that the solitary wave solutions of the KdV equation have the remarkable property of retaining their identities after collisions with other solitary waves. They gave these special waves the name "solitons." This discovery motivated a more detailed mathematical study of the KdV equation, including a search for conservation laws for the KdV equation which eventually led to devising the "inverse scattering method" for exact determination of the N-soliton solutions. In this talk, I will describe some of these discoveries and their histories. One feature I will demonstrate is that progress in science can be strongly influenced by non-scientific events and circumstances. These discoveries now have been extended and generalized to many different equations and applications, and a whole industry has developed pursuing these new directions.