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Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of discrete breather that exist at the atomic scale in a magnetic solid. Other observations of breathers refer to systems such as Josephson--junction arrays, photonic crystals and optical-switching waveguide arrays. All these observations underscore their importance in physical phenomena at all scales. The authors review some of their latest theoretical contributions in the field of classical and quantum breathers, with possible applications to these widely different physical systems and to many other such as DNA, proteins, quantum dots, quantum computing, etc.
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schrodinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it to calculate
We study the relations between solitons of nonlinear Schr{o}dinger equation described systems and eigen-states of linear Schr{o}dinger equation with some quantum wells. Many different non-degenerated solitons are re-derived from the eigen-states in t
Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity constituting a nonlinear lattice. Bright defect modes are supported by local increase of the nonlinearity,
We study localized solutions for the nonlinear graph wave equation on finite arbitrary networks. Assuming a large amplitude localized initial condition on one node of the graph, we approximate its evolution by the Duffing equation. The rest of the ne
We present an unifying description of a new class of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself. We show t