相关论文: Exact transparent boundary condition for the multi…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
We consider an explicitly solvable model (formulated in the Riemannian geometry terms) for a stationary wave process in a specific thin domain with the Dirichlet boundary conditions on the boundary of the domain. The transition from the…
An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averagings both in time and space.…
Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\"odinger-type equation posed on…
This work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science. Here we propose a new technique to force the positive…
We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space…
Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hidden from external observations. The…
The paper presents an automatic generator of approximate nonreflecting boundary conditions, analytical and numerical, for scalar wave equations. This generator has two main ingredients. The first one is a set of local Trefftz functions --…
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this…
The aim of this article is to prove an "almost" global existence result for some semilinear wave equations in the plane outside a bounded convex obstacle with the Neumann boundary condition.
In this paper, we consider the scattering of a time-dependent electromagnetic wave by an elastic body immersed in the lower half-space of a two-layered background medium which is separated by an unbounded rough surface. By proposing two…
Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within…
The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is…
In the prototypical setting of non-Euclidean geometry, the 2-dimensional Real Hyperbolic space $\mathbb{H}^2$, we consider the Carleson's problem for the Schr\"odinger equation and improve the best known result until now by proving that the…
We introduce a new type of boundary conditions, {\it smooth boundary conditions}, for numerical studies of quantum lattice systems. In a number of circumstances, these boundary conditions have substantially smaller finite-size effects than…
In this paper the concept of wave-guiding medium, previously introduced for planar structures, is defined for the spherically symmetric case. It is shown that a quarter-wavelength layer of such a medium serves as a transformer of boundary…
Historically, most of the quantum mechanical results have originated in one dimensional model potentials. However, Von-Neumann's Bound states in the Continuum (BIC) originated in specially constructed, three dimensional, oscillatory,…
Local perturbations of an infinitely long rod go away to infinity. On the contrary, in the case of a finite length of the rod, the perturbations reach its boundary and are reflected from it. The boundary conditions constructed here for the…