When attempting to understand the role of disorder in condensed-matter physics, we face
considerable experimental and theoretical difficulties, and many questions are still open …

The purpose of this review is to present a comprehensive and up-to-date account of the
main physical properties of DNA-based nanobiostructured devices, stressing the role played …

Recent results on theoretical studies of heat conduction in low-dimensional systems are
presented. These studies are on simple, yet non-trivial, models. Most of these are classical …

We report the observation of the signature of a localization phase transition for light in one-
dimensional quasiperiodic photonic lattices, by directly measuring wave transport inside the …

In the absence of nonlinearity all eigenmodes of a chain with disorder are spatially localized
(Anderson localization). The width of the eigenvalue spectrum and the average eigenvalue …

We consider the spatiotemporal evolution of a wave packet in disordered nonlinear
Schrödinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates …

We study the transport dynamics of matter-waves in the presence of disorder and
nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice …

Generalizations of the three main equations of quantum physics, namely, the Schrödinger,
Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by …

We study the critical behavior of Anderson localized modes near intersecting flat and
dispersive bands in the quasi-one-dimensional diamond ladder with weak diagonal disorder …

In the present work, we attempt a brief summary of various areas where non-linear waves
have been emerging in the phenomenology of lattice dynamical systems. These areas …