On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

Abstract

In this paper we study spatial analyticity of solutions to the defocusing nonlinear Schrödinger equations $i{u}_t+\Delta u=|u{|}^{p-1}u$, given initial data which is analytic with fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time $t$ cannot decay faster than $1/|t|$ as $|t|\to \infty$. This extends the previous work of Tesfahun for the cubic case $p=3$ to the cases where $p$ is any odd integer greater than $3$.

arXiv commentTo appear in Discrete Contin. Dyn. Syst., 18 pages

References in corpus (1)

• Almost conservation laws and global rough solutions to a Nonlinear Schrödinger equation

Cited by in corpus (1)

• Lower bounds on the radius of spatial analyticity for the Kawahara equation