Subdiffusion of nonlinear waves in two-dimensional disordered lattices

Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Straße 38, D-01187 Dresden, Germany, EU

^(a) lapteva@pks.mpg.de

Received: 14 March 2012
Accepted: 25 May 2012

Abstract

We perform high-precision computational experiments on nonlinear waves in two-dimensional disordered lattices with tunable nonlinearity. While linear wave packets are trapped due to Anderson localization, nonlinear wave packets spread subdiffusively. Various speculations on the growth of the second moment as t^α are tested. Using fine statistical averaging we find agreement with predictions from Flach S., Chem. Phys., 375 (2010) 548, which supports the concepts of strong and weak chaos for nonlinear wave propagation in disordered media. We extend our approach and find potentially long-lasting intermediate deviations due to a growing number of surface resonances of the wave packet.