Wave interactions in localizing media - a coin with many faces

Abstract

A variety of heterogeneous potentials are capable of localizing linear non-interacting waves. In this work, we review different examples of heterogeneous localizing potentials which were realized in experiments. We then discuss the impact of nonlinearity induced by wave interactions, in particular its destructive effect on the localizing properties of the heterogeneous potentials.

Review submitted to Intl. Journal of Bifurcation and Chaos Special Issue edited by G. Nicolis, M. Robnik, V. Rothos and Ch. Skokos 21 Pages, 8 Figures

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• Complex Statistics and Diffusion in Nonlinear Disordered Particle Chains
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using $q$-Statistics
• Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition
• Self-trapping threshold in disordered nonlinear photonic lattices
• Chaoticity without thermalisation in disordered lattices
• Quench-induced delocalization
• Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves
• Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices
• Frequency map analysis of spatiotemporal chaos in the nonlinear disordered Klein-Gordon lattice
• Wave-packet spreading in disordered soft architected structures