Asymptotics for the Camassa-Holm equation
44 mins 50 secs,
156.73 MB,
Windows Media Video
44100 Hz,
477.31 kbits/sec
About this item
| Description: |
Boutet de Monvel, A (Paris 7)
Wednesday 28 March 2007, 15:30-16:15 |
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| Created: | 2008-02-21 18:09 | ||
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| Collection: | Highly Oscillatory Problems: Computation, Theory and Application | ||
| Publisher: | Isaac Newton Institute | ||
| Copyright: | Boutet de Monvel, A | ||
| Language: | eng (English) | ||
| Credits: |
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| Abstract: | I will present recent results on asymptotic behaviors for the Ca-massa–Holm (CH) equation ut - utxx + 2?ux + 3uux = 2uxuxx + uuxxx on the line, ? being a nonnegative parameter.
Firstly, I will describe the long-time asymptotic behavior of the solution u? (x, t), ? > 0 of the initial-value problem with fast decaying initial data u0(x). It appears that u? (x, t) behaves differently in different sectors of the (x, t)-half-plane. Then I will analyse the behavior of u? (x, t) as ? 0. The methods are inverse scattering in a matrix Riemann-Hilbert approach and Deift and Zhou’s nonlinear steepest descent method. Work in collaboration with Dmitry Shepelsky. |
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