Nonlinear dynamics is about 400 some years old. European monarchs of the time cared about their ships surviving the rough Atlantic waves and thus Euler, Lagrange, Newton, Cauchy and many others worked on nonlinear wave equations (which presumably predate the linear wave equation!). In the nineteenth and twentieth centuries, nonlinear systems have been worked on in terms of continuum equations and we know that many of these (integrable) equations admit so-called soliton solutions where solitons are traveling, non-dispersive lumps of energy (almost like quanta but classical). In 1955, Fermi-Pasta-Ulam-Tsingou studied a nonlinear mass-spring chain and showed that the system has great trouble equilibrating. In 1983, Nesterenko first examined impulse propagation through an alignment of elastic grains and showed these systems too support solitons/solitary waves. Does the perturbed granular chain system equilibrate? What does it physically mean to have a non-integrable system? And why do we even care? The talk will touch upon the history and the current state of nonlinear physics of many particle systems and what all this physics can give us in terms of new scientific insights and novel technology.

Parts of this work has been supported over time by the National Science Foundation and the Army Research Office. Many of the calculations have been done on the supercomputers at the Center for Computational Research at SUNY Buffalo.