KARACHALIOS , Nikolaos I.

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We consider the question of existence of periodic solutions (called breather solutions or discrete solitons) for the Discrete Nonlinear Schrödinger Equation with saturable and power nonlinearity. Theoretical and numerical results are proved concerning the existence and nonexistence of periodic solutions by a variational approach and a fixed...

We propose analytical lower and upper estimates on the excitation threshold for breathers (in the form of spatially localized and time periodic solutions) in discrete nonlinear Schrödinger (DNLS) lattices with power nonlinearity. The estimation, depending explicitly on the lattice parameters, is derived by a combination of a comparison argument...

We discuss the existence of breathers and of energy thresholds for their formation in DNLS lattices with linear and nonlinear impurities. In the case of linear impurities we present some new results concerning important differences between the attractive and repulsive impurity which is interplaying with a power nonlinearity. These differences...

We discuss the existence of breathers and lower bounds on their power, in nonlinear Schrödinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed-point arguments, deriving lower bounds for the power which can serve as a threshold for the existence of breather solutions. Qualitatively, the...

The Salerno model is a discrete variant of the celebrated nonlinear Schr¨odinger (NLS) equation interpolating between the discrete NLS (DNLS) equation and completely integrable Ablowitz-Ladik (AL) model by appropriately tuning the relevant homotopy parameter. Although the AL model possesses an explicit time-periodic solution known as the...

In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events. Given the space-time localized nature of Peregrine solitons, this is a priori a nontrivial task. Our main tool in this effort will be the study of the spectral stability...

In this poster we show some recent results concerning discrete solitons in strong optical lattices, which can be described by the Discrete Nonlinear Schrödinger equation. These results are related to a variation of this equation including saturable nonlinearity terms, a feature throughoutly studied in nonlinear optics. After presenting the...

We study deterministic escape dynamics of the discrete Klein-Gordon model with a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and selected numerical illustrations, we first derive conditions for collapse of an initially excited single-site unit, for both the...