Propagation of radius of analyticity for solutions to a fourth order nonlinear Schr\”odinger equation

Achenef Tesfahun, Birilew Belayneh Tsegaw, Tegegne Getachew

2022

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DOI 10.22541/au.165898084.46557858/v1
Data confidence 70 medium
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Abstract

We prove that the uniform radius of spatial analyticity $\sigma(t)$ of solution at time $t$ to the one-dimensional fourth order nonlinear Schr\”odinger equation $$ i\partial_tu-\partial_x^4u =|u |^2u $$ cannot decay faster than $1/ \sqrt{t}$ for large $t$, given initial data that is analytic with fixed radius $\sigma_0$. The main ingredients in the proof are a modified Gevrey space, a method of approximate conservation law and a Strichartz estimate for free wave associated with the equation.