Propagation of Gevrey regularity over long times 
for the fully discrete Lie Trotter splitting scheme
applied to the linear Schrödinger equation

François Castella; Guillaume Dujardin

Displaying similar documents to “Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation”

Cubic Quasilinear wave equation and bilinear estimates

Hajer Bahouri, Jean-Yves Chemin (2000-2001)

Séminaire Équations aux dérivées partielles

Similarity:

On the hierarchies of higher order mKdV and KdV equations

Axel Grünrock (2010)

Open Mathematics

Similarity:

The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces ${\hat{H}}_{s}^{r} (ℝ)$ defined by the norm ${∥v_{0}∥}_{{\hat{H}}_{s}^{r} (ℝ)} : = {∥{〈ξ〉}^{s} \hat{v_{0}}∥}_{L_{ξ}^{r^{'}}}, 〈ξ〉 = {(1 + ξ^{2})}^{\frac{1}{2}}, \frac{1}{r} + \frac{1}{r^{'}} = 1$ . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ $\frac{2 j - 1}{2 r^{'}}$ . The proof uses an appropriate variant of the Fourier restriction norm method. A counterexample is discussed to show that the Cauchy problem for equations of this type is in general ill-posed in the C 0-uniform sense, if s < $\frac{2 j - 1}{2 r^{'}}$ . The results for r =...

Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation

Jerry L. Bona, Zoran Grujić, Henrik Kalisch (2005)

Annales de l'I.H.P. Analyse non linéaire

Similarity:

The projected single-particle Dirac operator for Coulombic potentials.

Jakubassa-Amundsen, D.H. (2005)

Documenta Mathematica

Similarity:

Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics

Othmar Koch, Christian Lubich (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We discuss the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of the time-dependent Schrödinger equation in quantum molecular dynamics. This method approximates the high-dimensional nuclear wave function by a linear combination of products of functions depending only on a single degree of freedom. The equations of motion, obtained the Dirac-Frenkel time-dependent variational principle, consist of a coupled system of low-dimensional nonlinear partial...