### Research Experience for Undergraduates (REU) Seminar

Title: Korteweg-deVries, Solitions, and all that

Speaker: **Amy Cohen-Corwin**, Rutgers University

Date: July 13, 2004 1 - 2 pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

This talk will be an introduction and survey of the mysteries of the
Korteweg-deVries equations (KdV). KdV was originnaly formulated in 1895
to model the long-time behavior of certain water waves on canals. It
succeeded in "predicting" the "great waves of translation" first described
by John Scott Russell in 1844. In the 1960's KdV reappeared in the
attempt to understand numerical simulations of certain phenomena in atomic
physics, simulations that unexpextedly did not show the expected
"equipartition of energy". Matematical investigation of those simulations
spurred many preogressively more "pure" mathematical investigations of
"completely intergrable systems" as well as a theory of "non-linear
Fourier transfors" which turned out to be useful for problems in fiber
optics and in ocean waves.