相关论文: Generic Short-Time Propagation of Sharp-Boundaries…

We consider the long-time behavior of solutions to the short-pulse equation. Using the method of testing by wave packets, we prove small data global existence and modified scattering.

The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly…

It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…

The paper contains a simplified and improved version of the results obtained by the authors earlier. Wave propagation is discussed in a network of branched thin wave guides when the thickness vanishes and the wave guides shrink to a one…

We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the…

Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with…

We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…

We consider an abstract wave equation with a propagation speed that depends only on time. We investigate well-posedness results with finite derivative loss in the case where the propagation speed is smooth for positive times, but…

We consider a reaction-diffusion equation in narrow random channels. We approximate the generalized solution to this equation by the corresponding one on a random graph. By making use of large deviation analysis we study the asymptotic wave…

It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic…

In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…

A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…

We study free string propagation in families of plane wave geometries developing strong scale-invariant singularities in certain limits. We relate the singular limit of the evolution for all excited string modes to that of the…

A detailed exposition of highly efficient and accurate method for the propagation of the time-dependent Schr\"odinger equation is presented. The method is readily generalized to solve an arbitrary set of ODE's. The propagation is based on a…

Elastic wave propagation is a century-old problem. Unlike on a flat manifold, analytical solution is not well established for a curved manifold. In this study we take a step towards building an analytical framework for solving the elastic…

One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this article I establish some very general bounds for reflection and transmission coefficients for one-dimensional…

We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…

In this article we reconsider the problem of the propagation of waves in a random medium in a kinetic regime. The final aim of this program would be the understanding of the conditions which allow to derive a kinetic or radiative transfer…

In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…

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…