Dispersion Estimates for One-dimensional Discrete Schrödinger and Wave Equations

Abstract

We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schrödinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide new results concerning scattering for one-dimensional discrete perturbed Schrödinger operators which are of independent interest. Most notably we show that the reflection and transmission coefficients belong to the Wiener algebra.

23 pages

References in corpus (4)

• Dispersive estimates for Schrodinger operators in dimensions one and three
• On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension
• Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation
• On asymptotic stability of standing waves of discrete Schrödinger equation in $\mathbb{Z}$

Cited by in corpus (15)

• Dispersion Estimates for One-Dimensional Discrete Dirac Equations
• Attractors of Hamilton nonlinear partial differential equations
• Dispersion Estimates for One-Dimensional Schrödinger Equations with Singular Potentials
• Dispersion Estimates for One-Dimensional Schrödinger and Klein-Gordon Equations Revisited
• Structure of Noncommutative Solitons: Existence and Spectral Theory
• Asymptotic stability of small bound state of nonlinear quantum walks
• Properties of the Scattering Matrix and Dispersion Estimates for Jacobi Operators
• Dispersion Estimates for the Discrete Laguerre Operator
• The limiting absorption principle for the discrete Wigner-von Neumann operator
• Continuous and discrete dynamical Schrödinger systems: explicit solutions
• Dynamics of Noncommutative Solitons II: Spectral Theory, Dispersive Estimates and Stability
• Zero Energy Scattering for One-Dimensional Schrödinger Operators and Applications to Dispersive Estimates
• Scattering Properties and Dispersion Estimates for a One-Dimensional Discrete Dirac Equation
• Dispersive estimate for quasi-periodic Schrödinger operators on 1-$d$ lattices
• Stabilization of small solutions of discrete NLS with potential having two eigenvalues