Related papers: Wave Packets and Coherent Structures for Nonlinear…
Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas…
The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schr\"odinger equation (NLS). Within the class of exact NLS…
We apply the averaging method to analyze spatio-temportal structures in nonlinear Schr\"odinger equations and thereby study the dynamics of quasi-one-dimensional collisionally inhomogeneous Bose-Einstein condensates with the scattering…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schroedinger-Poisson system. Here, we consider a multistream model representing a statistical mixture of N pure states, each described by a wavefunction.…
The dynamics of an initially localized wavepacket is studied for the generalized nonlinear Schroedinger Equation with a random potential, where the nonlinearity term is |\psi|^p*\psi and "p" is arbitrary. Mainly short times for which the…
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to…
For the Schr\"odinger equation with a cubic-quintic, focusing-defocusing nonlinearity in one space dimension, we prove the asymptotic stability of solitary waves for a large range of admissible frequencies. For this model, the linearized…
We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schr{\"o}dinger-like equations. The…
The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…
In this paper we numerically solve the time dependent Schr\"odinger equation for scenarios using wave packets. These examples include the free wave packet, which we use to show the difference between group and phase velocities, the packet…
We consider time-dependent nonlinear Schroedinger equations subject to smooth, lattice-periodic potentials plus additional confining potentials, slowly varying on the lattice scale. After an appropriate scaling we study the homogenization…
We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and…
A nonlinear evolution equation for wave packet surface gravity waves with variation in topography is revisited in this article. The equation is modeled by a spatial inhomogeneous nonlinear Schr\"odinger (NLS) equation with varying…
We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson…
The nonlinear dynamics of two co-propagating electrostatic wavepackets, characterized by different wavenumbers and amplitudes, in a 1D non-magnetized plasma fluid model is considered, from first principles. The original plasma model,…
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…
We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…
We study the wave front set of the solutions of the initial value problem for nonlinear Schr\"{o}dinger equations via wave packet transform. We give an sufficient condition which assures that the solutions is in Sobolev space of order s in…
We discuss the (in)stability of solitary waves for a quasi-linear Schr{\"o}dinger equation. The equation contains a quasi-linear term, responsible for a saturation effect, as well as a power nonlinearity. For different exponents of the…