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
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.