Colloquium March 23
Date: Friday March 23
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: Nghiem Nguyen of Perdue Univ
Title: Stability of Solitary Waves
Abstract
Consider a body of water of finite depth under the influence of
gravity, bounded below by a flat, impermeable surface. If viscous and
surface tension effects are ignored, and assuming that the flow is
incompressible and irrotational, the fluid motion is governed by the
Euler equations together with suitable boundary conditions on the
rigid surfaces and on the air-water interface. However, in many
practical engineering situations, the full Euler equations appear far
more complex than are necessary for the modeling purpose at hand.
Consequently, quite a few other approximate models have been proposed
for usage when certain restricted physical regimes are satisfied. A
regime that arises in practical situations is that of waves in a
channel of approximately constant depth h that are uniform across the
channel, and which are small amplitude and long wavelength, and such
that the associated nonlinear and dispersive effects are balanced.
Several of those models possess a special class of solutions
known as solitary-wave solutions. Solitary waves are localized
nonlinear waves with remarkable stability properties, preserving their
identity even after undergoing complex interactions. In consequence of
this, and because the issue is interesting in its own right, the topic
of stability of solitary-wave solutions has attracted considerable
attention during the last three decades.
In this talk, stability of solitary-wave solutions to some of
these models will be discussed. Some of the results are joint works
with J. Albert, J. Bona, M. Chen, Y. Liu and S. Sun.
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