Dispersive PDE

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On the soliton dynamics under a slowly varying medium for generalized KdV equations

by Claudio Muñoz | Versailles
Time: 14:10 — 15:00  (Tuesday, May. 25, 2010)
Location: BA6183, Bahen Center, 40 St George St
Abstract:
We consider the problem of the soliton propagation, in a slowly varying medium, for a generalized Korteweg - de Vries equations (gKdV). We study the effects of inhomogeneities on the dynamics of a standard soliton. We prove that slowly varying media induce on the soliton solution large dispersive effects at large time. Moreover, unlike gKdV equations, we prove that there is no pure-soliton solution in this regime.

Dates in this series

· Tuesday, May. 25, 2010: On the soliton dynamics under a slowly varying medium for generalized KdV equations (Claudio Muñoz)
· Tuesday, Jun. 22, 2010: Normal form and I-method (Tadahiro Oh)
· Monday, Jul. 26, 2010: Soliton resolution and action-angle coordinates for the Szego equation in the case of rational fraction initial data (Oana Pocovnicu)
· Monday, Jul. 26, 2010: Liouville-Arnold Theorem and action-angle coordinates (expository) (Oana Pocovnicu)
· Tuesday, Jul. 27, 2010: Quantized Poincare maps in chaotic scattering (Maciej Zworski)