Related papers: Wave packet dynamics for a non-linear Schrodinger …
We study the oscillations and conversions of relativistic neutrinos propagating in matter of variable density using the wave packet formalism. We show how the oscillation and coherence lengths are modified in comparison with the case of…
Interaction of linearized gravitational waves with a otherwise free particle has been studied quantum mechanically in a noncommutative phase-space to examine whether the particle's response to the gravitational wave gets modified due to…
We consider the Schrodinger equation with a generalized uncertainty principle for a free particle. We then transform the problem into a second ordinary differential equation and thereby obtain the corresponding propagator. The result of…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
This study employs spectral methods to capture the behaviour of wave equation with dispersive-nonlinearity. We describe the evolution of hump initial data and track the conservation of the mass and energy functionals. The…
The cubic nonlinear Schrodinger equation (NLS) in one dimension is considered in the presence of an intensity-dependent dispersion term. We study bright solitary waves with smooth profiles which extend from the limit where the dependence of…
The effect of the modulation instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schr\"odinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed…
We report on a number of careful numerical experiments motivated by the semiclassical (zero-dispersion, \epsilon\downarrow 0) limit of the focusing nonlinear Schr\"odinger equation. Our experiments are designed to study the evolution of a…
Non-dispersive wave packet for massless fermions is formulated on the basis of squeezed coherent states that are put in a form of common eigenfunction for the Hamiltonian and the helicity operator, starting from the Dirac equation. The wave…
We consider the semiclassical (zero-dispersion) limit of the one-dimensional focusing Nonlinear Schroedinger equation (NLS) with decaying potentials. If a potential is a simple rapidly oscillating wave (the period has the order of the…
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.…
The dynamics of two pairs of counter-propagating waves in two-component media is considered within the framework of two generally nonintegrable coupled Sine-Gordon equations. We consider the dynamics of weakly nonlinear wave packets, and…
We study the quantum evolution in dimension three of a system composed by a test particle interacting with an environment made of $N$ harmonic oscillators. At time zero the test particle is described by a spherical wave, i.e. a highly…
We derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity through a positive three-body potential.…
We investigate the effect of non-paraxiality in the dynamics of dispersive shock waves in the defocusing nonlinear Schroedinger equation. We show that the problem can be described in terms of a relativistic particle moving in a potential.…
We build Gaussian wave packets for the linear Schr\"odinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in Ignat, Zuazua,…
In this study, potential scatterings are formulated in experimental setups with Gaussian wave packets in accordance with a probability principle and associativity of products. A breaking of an associativity is observed in scalar products…
Squared deviations from the equilibrium positions of one-dimensional coupled harmonic oscillators with fixed and free endpoints are calculated, and the time averages are expressed as a function of the initial displacements and velocities.…
Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the…
Gravitational waves sourced by amplified scalar perturbations are a common prediction across a wide range of cosmological models. These scalar curvature fluctuations are inherently nonlinear and typically non-Gaussian. We argue that the…