Related papers: Spreading for the generalized nonlinear Schroeding…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
We consider the spreading of the wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of non-ergodic extended states $1<\gamma<2$. We show that despite non-trivial fractal dimensions $0 < D_{q}=2-\gamma<1$…
The nonlinear Schr\"odinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power…
Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic…
We derive an exact analytical solution to the time-dependent Schr\"odinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We study the spreading dynamics of an initially localized wave packet in 1D nonlinear Schr\"{o}dinger lattices with random potential. It is shown that adding small dielectric coupling to surrounding random medium results in asymptotic…
In this paper we study the behavior of solutions of a nonlinear Schroedinger equation in presence of an external potential, which is allowed to be singular at one point. We show that the solution behaves like a solitary wave for long time…
We study the time evolution of wave packets at the mobility edge of disordered non-interacting electrons in two and three spatial dimensions. The results of numerical calculations are found to agree with the predictions of scaling theory.…
In this paper, we consider the Schr\"odinger equation in one space-dimension with potential and we aim at exhibiting dynamic interaction phenomena produced by the potential. To this end, we focus our attention on the time-asymptotic…
We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{\sigma} u_{l}$ for different values of $\sigma$. We perform extensive numerical simulations where wave…
We establish the probabilistic well-posedness of the nonlinear Schr\"odinger equation on the $2d$ sphere $\mathbb{S}^{2}$. The initial data are distributed according to Gaussian measures with typical regularity $H^{s}(\mathbb{S}^{2})$, for…
An analytical approach to quantum mechanical wave packet dynamics of laser-driven particles is presented. The time-dependent Schroedinger equation is solved for an electron exposed to a linearly polarized plane wave of arbitrary shape. The…
Thermalization of systems described by the discrete non-linear Schr\"odinger equation, in the strong disorder limit, is investigated both theoretically and numerically. We show that introducing correlations in the disorder potential, while…
Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity…
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…
We consider the Schroedinger equation with a general interaction term, which is localized in space. The interaction may be x, t dependent and non-linear. Purely non-linear parts of the interaction are localized via the radial Sobolev…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
In the absence of nonlinearity all normal modes (NMs) of a chain with disorder are spatially localized (Anderson localization). We study the action of nonlinearity, whose strength is ramped linearly in time. It leads to a spreading of a…
We probe the limits of nonlinear wave spreading in disordered chains which are known to localize linear waves. We particularly extend recent studies on the regimes of strong and weak chaos during subdiffusive spreading of wave packets [EPL…