PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Hope Shaffer, Chun Liu.

Title:Solitary waves in lattices: an introduction
Seminar:CCMA Luncheon Seminar
Speaker:Anna Vainchtein, University of Pittsburgh (Host: X Li)
Abstract:
The interplay between discreteness and nonlinearity in many physical systems leads to the formation of solitary waves. For example, such waves were experimentally observed in granular materials, electrical transmission lines and optical fibers. Much of the interest in these nonlinear waves was triggered by the pioneering study by Fermi, Pasta and Ulam (1955). The subsequent work of Zabusky and Kruskal (1965) has revolutionized the nonlinear science by connecting the FPU problem to its continuum near-sonic limit described by the KdV equation. In integrable systems solitary waves, known as solitons, are now well understood, with one-dimensional Toda lattice being the most prominent example that has an exact solution covering a broad range of behaviors from delocalized low-energy waves in the KdV limit to highly localized high-energy waves. Most discrete systems, however, are non-integrable. In this case understanding the transition from the KdV limit to the strongly discrete waves has mostly relied on numerical and quasicontinuum approximations. In this introductory talk I will describe some of the important developments in this area.

Room Reservation Information

Room Number:MB114
Date:12 / 08 / 2014
Time:12:20pm - 01:30pm