相关论文: Dispersion for 1-d Scrodinger and wave equation wi…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
For the one dimensional nonlinear Schr\"odinger equation with triple power nonlinearity and general exponents, we study analytically and numerically the existence and stability of standing waves. Special attention is paid to the curves of…
We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the constant direction are known to evolve into solitary waves, due…
It is common for dispersion curves of damped periodic materials to be based on real frequencies versus complex wavenumbers or, conversely, real wavenumbers versus complex frequencies. The former condition corresponds to harmonic wave motion…
This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is…
It is demonstrated that -- contrary to the common belief -- it is possible to construct solutions of the non-relativistic Schr\"odinger equation of a free particle, that do not exhibit dispersion. However, it seems that no normalizable wave…
We study the existence and stability of periodic traveling-wave solutions for the quadratic and cubic nonlinear Schr\"odinger equations in one space dimension.
We demonstrate that mechanical waves traveling in a torsional, mechanical wave machine exhibit dispersion due to gravity and the discreteness of the medium. We also show that although the dispersion due to discreteness is negligible, the…
The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…
This paper aims to give a general (possibly compact or noncompact) analog of Strichartz inequalities with loss of derivatives, obtained by Burq, G\'erard, and Tzvetkov [19] and Staffilani and Tataru [51]. Moreover we present a new approach,…
It is known that Schr\"odinger equation fails in describing the dynamics of highly energetic particles. We propose to quantify this lack of Lorentz covariance by evaluating the probability for a particle to be measured outside the set of…
The effect of the small dispersion on the self-focusing of solutions of the equations of nonlinear geometric optics in one-dimensional case is investigated. In the main order this influence is described by means of the universal special…
A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential…
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,…
This article is concerned with one dimensional dispersive flows with cubic nonlinearities on the real line. In a very recent work, the authors have introduced a broad conjecture for such flows, asserting that in the defocusing case, small…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
In two prior papers of this series, it was proposed that a wavefunction model of a heavy particle and a collection of light particles might generate ``Brownian-Motion-Like" trajectories as well as diffusive motion (displacement proportional…
We prove smoothing estimates for Schr\"odinger equations $i\partial_t \phi+\partial_x (a(x) \partial_x \phi) =0$ with $a(x)\in \mathrm{BV}$, the space of functions with bounded total variation, real, positive and bounded from below. We then…
We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we…
Large deviation principle by the weak convergence approach is established for the stochastic nonlinear Schrodinger equation in one-dimension and as an application the exit problem is investigated.