"Localized waves in granular crystals"
<br>
<br>
Granular crystals consist of a collection of masses (typically steel beads)
arranged on a regular lattice and interacting nonlinearly by contact. These
systems display different types of nonlinear wave phenomena, such as the
formation of localized waves (solitary waves or breathers) after an impact. The
wave dynamics is strongly influenced by lattice properties (type of discrete
elements, existence of confining potentials, precompression), which opens
interesting possibilities to control stress waves. Granular crystals can be
modeled by different types of lattice differential equations depending on their
structural properties. In particular, one-dimensional granular chains can lead
to the Fermi-Pasta-Ulam (FPU) model with Hertzian potential, mixed
FPU-Klein-Gordon lattices or the discrete p-Schrödinger equation, a new
asymptotic model obtained when confining potentials are present. We will
illustrate the rich properties of localized waves in these models through
numerical simulations and analytical results.