Workshop on Soliton Equations: Applications and Theory

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NSF Award Abstract - DMS-0104337Mathematical Sciences: Workshop on Soliton Equations: Applications and TheoryAbstract0104337 CarlsonThis award supports U.S. participants (primarily young researchers and graduate students) in the Workshop on Soliton Equations: Applications and Theory, held at the University of Colorado, Colorado Springs, on August 10-12, 2001. The workshop involves interdisciplinary examination of soliton equations by experts in both theory and applications. Nonlinear problems of optical communications are emphasized, particularly the use of the nonlinear Schroedinger equation and its variants for the modeling and design of long distance fiber optic communication systems. Additional applied topics include the appearance of solitons in other optical problems, magnetic thin films, and Bose-Einstein condensates. Theoretical topics include extensions of inverse scattering and inverse spectral theory to Schroedinger or Dirac type operators, new methods of analyzing Riemann-Hilbert problems, connections of soliton equations with geometry, and new insights into meromorphic or real analytic solutions of soliton equations. Since the initial discoveries relating the Korteweg - de Vries equation to the scatteringtransform, soliton equations have provided a veritable fountain of physical and mathematical surprises. This workshop offers researchers in this field a chance to exchange new results and new problems, and it provides young researchers with an overview of the field. The workshop aims at interdisciplinary presentation, with a healthy mix of successful applications of the ideas to physical problems, computational studies which can illuminate applications and suggest new theoretical issues, and new theoretical results.