On the persistence of spatial analyticity for generalized KdV equation with higher order dispersion

Tegegne Getachew, Achenef Tesfahun, Birilew Belayneh Tsegaw

2023

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DOI 10.1002/mana.202300158
Data confidence 70 medium
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Abstract

Abstract Persistence of spatial analyticity is studied for solutions of the generalized Korteweg‐de Vries (KdV) equation with higher order dispersion where , are integers. For a class of analytic initial data with a fixed radius of analyticity , we show that the uniform radius of spatial analyticity of solutions at time cannot decay faster than as . In particular, this improves a recent result due to Petronilho and Silva [Math. Nachr. 292 (2019), no. 9, 2032–2047] for the modified Kawahara equation (, ), where they obtained a decay rate of order . Our proof relies on an approximate conservation law in a modified Gevrey spaces, local smoothing, and maximal function estimates.