Related papers: The Dispersion property for Schr\"odinger equation…
We introduce new models for Schr\"odinger-type equations, which generalize standard NLS and for which different dispersion occurs depending on the directions. Our purpose is to understand dispersive properties depending on the directions of…
We prove a general dispersive estimate for a Schroedinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates. Among the applications are the…
The discrete Schr\"odinger equation on a two-dimensional honeycomb lattice is a fundamental tight-binding approximation model that describes the propagation of waves on graphene. For free evolution, we first show that the degenerate…
We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted…
We consider the Schroedinger operator in R^3 with N point interactions placed at Y=(y_1, ... ,y_N), y_j in R^3, of strength a=(a_1, ... ,a_N). Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove a…
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 study the free Schr\"odinger equation on finite metric graphs with infinite ends. We give sufficient conditions to obtain the $L^1$ to $L^\infty$ time decay rate at least $t^{-1/2}$. These conditions allow certain metric graphs with…
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,…
We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive…
In this paper, we investigate quantitative propagation of smallness properties for the Schr\"odinger operator on a bounded domain in $\mathbb R^d$. We extend Logunov, Malinnikova's results concerning propagation of smallness for…
Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.
We prove the dispersive and Strichartz estimates for solutions to the wave equation with a class of many-electric potentials in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the…
We study the decay and smoothness of solutions of the dispersion managed non-linear Schr\"odinger equation in the case of zero residual dispersion. Using new x-space versions of bilinear Strichartz estimates, we show that the solutions are…
We prove dispersive and Strichartz estimates for Schr\"o- dinger equations on a class of locally symmetric spaces {\Gamma}\X, where X = G/K is a symmetric space and {\Gamma} is a torsion free discrete sub- group of G. We deal with the cases…
In this paper we obtain minimal support properties of solutions of Schr\"odinger equations. We improve previously known conditions on the potential for which the measure of the support of solutions cannot be too small. We also use these…
We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this…
We give a survey on recent developments on nonlinear Schr\"odinger equations with dissipative structure based on the authors' recent works.
The properties of pulse propagation in a nonlinear fiber including linear damped term added in the usual nonlinear Schr\"odinger equation is analyzed analytically. We apply variational modified approach based on the lagrangian that describe…
In this paper we analyze the dispersion for one dimensional wave and Schrodinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient…
We consider the spectrum of the discrete Schr\"odinger equation with one-dimensional perturbation. We obtain the explicit form of scattering matrix and find the exact condition of absence of singular part of the spectrum. We calculated also…