Title: Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model
Speaker: Gene Wayne
Speaker Info: Boston University
Brief Description:
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Abstract:
Recently methods have been developed with permit one to rigorously justify the use of ``amplitude'' or ``modulation'' equations that arise in a wide variety of physical contexts. In particular, Guido Schneider and I have recently shown that over the time and length scales commonly used to derive long-wave equations for fluid surfaces, the irrotational motion of an incompressible, inviscid fluid of finite depth can be described by a pair of uncoupled Korteweg-de Vries equations. In this talk I will review this result, describe the general method of proof, and apply this method in another context to show that in an appropriate scaling, the motion of the Fermi-Pasta-Ulam model of coupled, nonlinear oscillators can also be approximated by a pair of uncoupled KdV equations.Date: Friday, February 9, 2001