Related papers: Intrinsic localized modes in parametrically-driven…
We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the…
It is well known that the two-dimensional (2D) nonlinear Schr\"odinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity supports a family of stable fundamental solitons, as well as solitary vortices (alias vortex rings), which are…
In the current work we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we study the…
We derive and study a simple 1D nonlinear model for Edge Localized Mode (ELM) cycles. The nonlinear dynamics of a resistive ballooning mode is modeled via a single nonlinear equation of the Ginzburg-Landau type with a radial frequency…
We study numerically the nonintegrable dynamics of coherent, solitonic, nonlinear waves, in a spatially nonlocal nonlinear Schrodinger equation relevant to realistic modelling of optical systems: the Schrodinger-Helmholtz equation. We…
We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schr\"{o}dinger equation (NLSE), which includes a small quintic term, and weak resonant nonlinearity management (NLM),…
We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schr\"{o}dinger (DNLS) equations with the attractive self-phase-modulation (SPM) nonlinearity, coupled…
The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev-Petviashvili (enKP) model through a systematic analysis of…
Type-I Edge Localised Modes (ELMs) have been mitigated in MAST through the application of n = 3, 4 and 6 resonant magnetic perturbations (RMPs). For each toroidal mode number of the non-axisymmetric applied fields, the frequency of the ELMs…
In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\"odinger equation…
IN-DNLS, considered here is a countable infinite set of coupled one dimensional nonlinear ordinary differential difference equations with a tunable nonlinearity parameter, $\nu$. This equation is continuous in time and discrete in space…
In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete…
We construct a description of Ion Temperature Gradient (ITG) driven localised linear modes which retains both wave-particle and magnetic drift resonant effects while capturing the field-line dependence of the electrostatic potential. We…
Employing a particularly suitable higher order symplectic integration algorithm, we integrate the 1-$d$ nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an…
The possibility of thermal excitation of intrinsic localized modes (ILMs) arising from anharmonicity in ionic perfect crystals is studied numerically for realistic model systems in one and three dimensions. Implications are discussed for an…
In this paper, the vibration energy localization in coupled nonlinear oscillators is investigated, based on the creation of standing solitons. The main objective is to establish a design methodology for mechanical lattices using the…
Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of…
The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation.…
We consider nonlinear modes of the nonlinear Schr\"odinger equation with a nonlocal nonlinearity and an additional PT-symmetric parabolic potential. We show that there exists a set of continuous families of nonlinear modes and study their…
Phenomenological studies of cosmic-ray self-confinement often hinge on the linear theory for the growth rate of the streaming instability and for the damping rate of the generated magnetic modes. Largely different expressions exist,…