Solitary Waves in Layered Nonlinear Media Randall J. LeVeque University of Washington One-dimensional plane waves in an elastic material can be modelled by a hyperbolic system of partial differential equations. In a homogeneous material, a nonlinear stress-strain relation leads to the formation of shock waves. Instead consider a laminated medium that consists of alternating layers of two different nonlinear materials. In this case the wave is partially reflected at each material interface, leading to dispersion and more complicated wave behavior. This dispersion, coupled with the nonlinearity, sets the stage for the appearance of solitary waves that behave like solitons in many respects. I will present some computational results based on solving the hyperbolic system directly in the layered medium, and briefly discuss the high-resolution numerical methods used for such computations. I will also present some nonlinear homogenization results of Darryl Yong that yield an accurate effective equation containing dispersive terms.