This analysis clarifies the limitations of the analyticity radius in nonlinear Schrödinger equations, suggesting implications for defocusing scenarios.
We consider the initial value problem associated to the fourth-order nonlinear Schrödinger equation in the defocusing scenario :[Formula: see text] where [Formula: see text], [Formula: see text] be an odd integer, [Formula: see text], and the initial data [Formula: see text] is analytic in a strip around the [Formula: see text]-axis of the complex plane and has uniform radius of spatial analyticity [Formula: see text]. It is shown that the analyticity radius [Formula: see text] of solutions as time [Formula: see text] goes to infinity does not decay faster than [Formula: see text]. Our strategy mainly relies on a method of approximate conservation law in a modified Gevrey spaces, biharmonic Schrödinger admissibility, Strichartz estimates and Sobolev embedding.
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Tegegne Getachew (2025) studied this question.
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