Applied Math Seminar: Granular chains and the logarithmic KdV equation
Dmitry Pelinovsky, McMaster University
Event: Applied Mathematics Seminar
Date and time: Thursday Jan 26, 2017 3:30 pm
Where: Arts 134
Speaker: Professor Dmitry Pelinovsky, McMaster University
Title: "Granular chains and the logarithmic KdV equation"
Abstract:
"Granular chains of particles coupled by Hertzian forces are modeled the Fermi–Pasta–Ulam (FPU) lattices with fractional power nonlinearity. Solitary waves in such strongly nonlinear systems without pre-compression have fast (double-exponential) decay. I will discuss the asymptotic limit, where the FPU lattice can be reduced formally to the logarithmic Korteweg–de Vries (KdV) equation which possesses linearly orbitally stable Gaussian solitary waves. I will overview the existence and stability problems in the time evolution of the logarithmic KdV equation and the associated difficulties in the justification of this approximation."
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