JON GRUE:
"Lax-pairs, and solitons in theory and practice."
The lecture will start with a brief review of the paper by Zabusky and Kruskal (1965) where the notion of soliton was introduced. The landmark paper by Gardner, Greene, Kruskal and Miura (1967) on the inverse scattering theory, leading also to practical evaluation of soliton solutions of the KdV-equation, expressing the wave amplitude and volume in terms of the eigenvalue(s) is then discussed. There exist an infinite number of integral invariants of the KdV equation: the first three were found by Boussinesq, two more were found by Zabusky and Kruskal, and Miura, Gardner and Kruskal showed in 1968 the existence of the an infinite number of integral invariants, and how to evalue them. The role of the Lax-pairs (Lax, 1968) in soliton theory will be emphasized through the talk. The works by Zakharov and Shabat (1971 and onwards) will be mentioned. At the end of the talk, a brief introduction to solitons in practice will be given: It is so that the only solitons that are not man-made, exist in the form internal solitons in the ocean. The waves exhibit a very pronounced natural phenomenon. This was first discovered in large extent during the sixties and seventies as a result of the American and Russian space programs. The timing of the discovery of these waves, and that of the very intense research on integrable nonlinear partial differentional equations, is interesting! The waves are typcally a couple of kilometers long, have amplitudes of the order 100 meters, and exhibit a strongly nonlinear behaviour that is usually outside the range of KdV or BO theories. Equations are typically nonintegrable. Experiments and theory on the waves make a lot of fun for fluid mechanicians, as well as the waves make a concern for industries operating in deep water.
Everybody is invited to a demo of internal solitons in the laboratory after the talk.
1430-1530 i pausearealet i 7. etage og laboratoriet i kjelleren
Kaffe og kjeks fra kl 1400