Related papers: Dispersive Properties for Discrete Schrodinger Equ…
We prove exponential decay for a system of two Schr{\"o}dinger equations in a wave guide, with coupling and damping at the boundary. This relies on the spectral analysis of the corresponding coupled Schr{\"o}dinger operator on the…
This paper deals with global dispersive properties of Schr\"odinger equations with real-valued potentials exhibiting critical singularities, where our class of potentials is more general than inverse-square type potentials and includes…
We prove a dispersive estimate for the one-dimensional Schroedinger equation, mapping between weighted $L^p$ spaces with stronger time-decay ($t^{-3/2}$ versus $t^{-1/2}$) than is possible on unweighted spaces. To satisfy this bound, the…
A new decomposition for frequency-localized solutions to the Schrodinger equation is given which describes the evolution of the wavefunction using a weighted sum of Lipschitz tubes. As an application of this decomposition, we provide a new…
By the multiple-scale method some new approximate absorbing boundary conditions for the Schr\"odinger type equations are obtained.
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…
This paper describes a new comparison principle that can be used for the comparison of space-time estimates for dispersive equations. In particular, results are applied to the global smoothing estimates for several classes of dispersive…
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schr\"odinger equations with a real drift.
We prove the convergence in a strong norm of a finite difference semi-discrete scheme approximating a coupled Schr\"odinger--KdV system on a bounded domain. This system models the interaction of short and long waves. Since the energy…
We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on the duality principle and the smooth perturbation theory…
Discrete variational methods show excellent performance in numerical simulations of mechanical systems. In this paper, we adapt discrete variational integrators for the case of mechanical systems with double-bracket dissipation. In…
We prove that the solution of certain linear stochastic differential equations in Hilbert spaces, namely those with bounded operators as well as the conservative stochastic Schr\"odinger equations, can be obtained - along the lines of the…
In this paper, we study one-dimensional linear Schr\"odinger equations with multiple moving potentials, known as transfer charge models. Focusing on the non-self-adjoint setting that arises in the study of solitons, we systematically…
We prove optimal high-frequency resolvent estimates for perturbations by large magnetic and electric potentials
We consider the dispersion managed nonlinear Schr\"odinger equation with power-law nonlinearity and its discrete version of equations with step size $h\in(0,1]$. We prove that the solutions of the discrete equations strongly converge in…
In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients…
In this expository note, we prove some extensions and refinements of classical Kato type estimates with elementary techniques.
We prove a decay estimate for an operator that arises in two-dimensional scattering problem.
We present general results on exponential decay of finite energy solutions to stationary nonlinear Schr\"odinger equations.
For a large class of complete, non-compact Riemannian manifolds, $(M,g)$, with boundary, we prove high energy resolvent estimates in the case where there is one trapped hyperbolic geodesic. As an application, we have the following local…