Inverse problem for multi-body interaction of nonlinear waves.

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers.

Heterogeneous shear elasticity of glasses: the origin of the boson peak.

The local elasticity of glasses is known to be inhomogeneous on a microscopic scale compared to that of crystalline materials. Their vibrational spectrum strongly deviates from that expected from Debye's elasticity theory: The density of states deviates from Debye's law, the sound velocity shows a negative dispersion in the boson-peak frequency regime and there is a strong increase of the sound attenuation near the boson-peak frequency. By comparing a mean-field theory of shear-elastic heterogeneity with a large-scale simulation of a soft-sphere glass we demonstrate that the observed anomalies in glasses are caused by elastic heterogeneity.