Applied Mathematics Colloquium | |||
| Date: | November 10, 2009 from 2:45 pm to 3:45 pm EST | ||
| Location: | Columbia University Morningside Campus S.W. Mudd Building, Room 214 |
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| Contact: | For further information regarding this event, please contact APAM Department by sending email to seasinfo.apam@columbia.edu or by calling 212-854-4457. | ||
| Info: | Click Here to Visit Website. | ||
Vadim Zharnitsky KdV equation is a standard model of weakly nonlinear long waves on the surface of shallow water. It will be shown that in KdV with periodic boundary conditions, high frequency solutions evolve almost as the linear ones for large time. For KdV (or some other dispersive equations) on the real line such behavior could be expected due to the dispersive decay. While on the circle (i.e. periodic boundary conditions) such dispersive decay is not possible, the dispersion manifests itself in averaging out nonlinearity over high frequency solutions. This result is obtained by the application of normal form transformations in the appropriate spaces. The integrability properties of KdV are not used, so similar results could be obtained for other KdV like equations. The interaction of these high frequency solutions with a cnoidal wave will be discussed, too. This work has been motivated by an attempt to explain some phenomena in nonlinear optics and fluid dynamics. This is a joint work with M.B. Erdogan and N. Tzirakis (also University of Illinois). Host: Michael Weinstein |
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