The University of Arizona
Please note that this event has ended!

Long-time dynamics of the modified KdV equation

Special Colloquium

Long-time dynamics of the modified KdV equation
Series: Special Colloquium
Location: MATH 402
Presenter: Gong Chen, University of Toronto

With the advent of computers in the middle of the 20’th century, through
the remarkable computations of Fermi-Pasta-Ulam (mid 50s) and
Kruskal-Zabusky (mid 60s) it was observed numerically that nonlinear
equations modeling wave propagation asymptotically exhibit as
superposition of “traveling waves” and “radiation”. This has become
known as the “soliton resolution conjecture”. This conjecture, roughly
speaking, says that any reasonable solution to a disperive equation 
eventually resolves into a superposition of a radiation component plus a
finite number of "nonlinear bound states"  or "solitons".  After an
informal introduction to dispersive equations, I will discuss the
soliton resolution and long-time dynamics for the modified Korteweg-de
vries (mKdV) equation with initial conditions in some weighted Sobolev
spaces combing ideas from integrable systems and partial differential
equations (PDEs).

(Refreshments will be served at 1pm in the Math Commons Room)