Solitons - A new paradigm in mathematical physics
Sir Michael Atiyah, University of Edinburgh
97th Kelvin Prestige Lecture Speaker: Sir Michael Atiyah, University of Edinburgh
09 March 2006 Control & Automation channel
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About the presentation
Sir Michael Atiyah surveys this exciting field which provides a whole new way of studying important and varied physical phenomena, where sophisticated mathematical ideas can be brought to bear and where contact between experiment, simulation and theory can be very fruitful. The traditional billiard ball of Newtonian mechanics or the more idealized notion of a point-particle has been a central paradigm of mathematics and physical science for centuries. Competing uneasily with this, in more recent times, has been the concept of a field propagating wave-like through space. In the past fifty years a new paradigm has appeared, the soliton, which is the term that has been coined for a wave that can behave like a particle. This idea has spread widely through physics and engineering and has attracted the increasing attention of mathematicians.
About the speaker
The soliton, as a physical phenomenon, made its dramatic debut in the 19th century as a solitary wave (or lump) of water on an Edinburgh Canal, pursued (on horseback) by the famous Scottish engineer John Scott Russell. Since that time solitons, both practical and theoretical, have turned up in a wide variety of areas including signal propagation along optic fibres - a topic that would undoubtedly have interested Lord Kelvin. The key facts about solitons are that they are highly-localized non-linear waves which exhibit the stability which we associate to particles or bodies. This includes collisions or interactions, though the collision process is more involved than with billiard balls. Sir Michael will illustrate this pictorially in his lecture.