Related papers: Phase Space Evolution and Discontinuous Schr\"odin…
We consider the Riemann problem of evolution of initial discontinuities for the photon fluid propagating in a normal dispersion fiber with account of self-steepening effects. The dynamics of light field is described by the nonlinear…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
We present the full classification of wave patterns evolving from an initial step-like discontinuity for arbitrary choice of boundary conditions at the discontinuity location in the DNLS equation theory. In this non-convex dispersive…
Refraction, interference, and diffraction serve as distinguishing features for wave-like phenomena. While they are normally associated only with a purely spatial wave-propagation pattern, analogs to interference and diffraction involving…
Although diffractive spreading is an unavoidable feature of all wave phenomena, certain waveforms can attain propagation-invariance. A lesser-explored strategy for achieving optical selfsimilar propagation exploits the modification of the…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
A problem in nonlinear water-wave propagation on the surface of an inviscid, stationary fluid is presented. The primary surface wave, suitably initiated at some radius, is taken to be a slowly evolving nonlinear cylindrical wave (governed…
Analytic solutions to the time-dependent Schr\"odinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential…
A separable $x-y$ model is solved for a specialized vector potential (no magnetic and weak electric fields) penetrating slowly\textbf{,} adiabatically into and across a rectangular box to which an electron is confined. The time-dependent…
The propagation of a wave-packet in a nonlinear disordered medium exhibits interesting dynamics. Here, we present an analysis based on the nonlinear Schr\"odinger equation (Gross-Pitaevskii equation). This problem is directly connected to…
Coherent states play an important role in quantum mechanics because of their unique properties under time evolution. Here we explore this concept for one-dimensional repulsive nonlinear Schr\"odinger equations, which describe weakly…
Diffraction in time manifests itself as the appearance of probability-density fringes when a matter wave passes through an opaque screen with abrupt temporal variations of transmission properties. Here we analytically describe the…
In the Schr\"odinger evolution of a quantum state time enters as a real parameter representing the coordinate. In a more consistent approach time should be defined as a quantum observable, with the evolution taking place in a…
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…
We analyze the matter wave transmission above a step potential within the framework of the cubic-nonlinear Schr\"odinger equation. We present a comprehensive analysis of the corresponding stationary problem based on an exact second-order…
This thesis deals with some theoretical aspects of deterministic freak wave generation in the wave basin of a hydrodynamic laboratory. We adopt the spatial nonlinear Schr\"odinger equation as a mathematical model to describe the deformation…
We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…
In this paper, we study the long time dynamics of small solutions to Schr\"odinger map flows from $\Bbb R$ to Riemannian surfaces. The results are threefold. (i) We prove that for general Riemannian surface targets the points with some…
The interface problem for the linear Schr\"odinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the…