Related papers: Dispersion estimates for 1D discrete equations
We prove spacetime weighted-L^2 estimates for the Schrodinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.
We investigate dispersive estimates for the Schr\"odinger operator $H=-\Delta +V$ with $V$ is a real-valued decaying potential when there are zero energy resonances and eigenvalues in four spatial dimensions. If there is a zero energy…
A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution satisfies the discrete Hestenes equation…
In this paper, we study the dispersive decay estimates for solution to the $3\mathrm{D}$ energy-critical nonlinear Schr\"odinger equation with an inverse-square operator $\mathcal{L}_a$ where the operator is denoted by…
A 3D singular integral equation is derived for electromagnetic wave scattering by bodies of arbitrary shape. Its numerical solution by a projection method is outlined.
We derive exact solutions to the one-dimensional Schr\"odinger equation for compact support parabolic and hyperbolic secant potential barriers, along with combinations of these types of potential barriers. We give the expressions for…
The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in…
In this paper, we derive sufficient conditions for each component of the solution to a general backward stochastic differential equation to have a density for which upper and lower Gaussian estimates can be obtained.
We study the asymptotics of the Schr\"odinger equation with time-dependent potential in dimension one. Assuming that the potential decays sufficiently rapidly as $|x| \to \infty$, we prove that the solution can be written as the sum of a…
Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.
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…
In this paper we study Strichartz estimates for dispersive equations which are defined by radially symmetric pseudo-differential operators, and of which initial data belongs to spaces of Sobolev type defined in spherical coordinates. We…
We study the orbital stablity and instability of solitary wave solutions for nonlinear Schr\"odinger equations of derivative type.
We study the decay properties of non-negative solutions to the one-dimensional defocusing damped wave equation in the Fujita subcritical case under a specific initial condition. Specifically, we assume that the initial data are positive,…
We prove spatiotemporal algebraically decaying estimates for the density of the solutions of the linearly damped nonlinear Schr\"odinger equation with localized driving, when supplemented with vanishing boundary conditions. Their derivation…
We obtain a dispersive long-time decay in weighted energy norms for solutions of the Klein-Gordon equation in a moving frame. The decay extends the results of Jensen, Kato and Murata for the equations of the Schr\"odinger type. We modify…
Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately…
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…
We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity…
Consider the one-dimensional discrete Schr\"odinger operator $H_{\theta}$: $$(H_{\theta} q)_n=-(q_{n+1}+q_{n-1})+ V(\theta+n\omega) q_n \ , \quad n\in Z \ ,$$ with $\omega\in R^d$ Diophantine, and $V$ a real-analytic function on $ T^d=(…