Related papers: Perfectly matched layers for the stationary Schrod…
By the multiple-scale method some new approximate absorbing boundary conditions for the Schr\"odinger type equations are obtained.
We present a numerical approach to the solution of elastic phonon scattering problems based on a frequency domain decomposition of the atomistic equations of motion and the use of perfectly matched layer or PML boundaries. Unlike MD…
In this work, we study the transmission properties of one dimensional finite periodic systems with $\mathcal{PT}$-symmetry. A simple closed form expression is obtained for the total transmittance from a lattice of N cells, that allows us to…
By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in presence of a quaternionic step potential. The analytic solution for the stationary states allows to…
We investigate wavepacket solutions for time-dependent Schoedinger equation in the presence of an exponentially decaying potential. Assuming for travelling wave solutions the phase to be a linear combination of the space and time…
Absorbing boundaries are frequently employed in real-time propagation of the Schr\"odinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an…
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr\"odinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are…
In this work, we obtained exact solutions of Einstein's field equations for plane symmetric cosmological models by assuming that thy admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic way. We obtain a deterministic limit shape in the scaling…
For Schr\"odinger equations with a class of slowly decaying repulsive potentials, we show that the solution satisfies global-in-time Strichartz estimates for any admissible pairs. Our admissible class of potentials includes the positive…
We show that an arbitrary body or aggregate can be made perfectly absorbing at discrete frequencies if a precise amount of dissipation is added under specific conditions of coherent monochromatic illumination. This effect arises from the…
We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.
For certain one-dimensional Schroedinger-type difference operators with a complex potential, a "complete" set of exponentially decaying eigenvectors is shown to exist. "Completeness" entails that the parameters involved are obtained through…
We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our…
A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is…
We study uniqueness for solutions to the Cauchy problem associated with the parabolic Schr\"odinger equation on complete noncompact Riemannian manifolds, under suitable integral conditions on the solution. We show that, under suitable…
We study the existence of stationnary positive solutions for a class of nonlinear Schroedinger equations with a nonnegative continuous potential V. Amongst other results, we prove that if V has a positive local minimum, and if the exponent…
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…
We study positive bound states for the semiclassical stationary nonlinear Schr\"odinger equation. We are especially interested in solutions which concentrate on a lower dimensional sphere. We adopt a purely variational approach which allows…