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

Getachew T. Tesfahun A. Belayneh B.
May 2024 John Wiley and Sons Inc

Mathematische Nachrichten
2024 #297 Issue 5 1737 - 1748 pp.

Persistence of spatial analyticity is studied for solutions of the generalized Korteweg-de Vries (KdV) equation with higher order dispersion (Formula presented.) where (Formula presented.), (Formula presented.) are integers. For a class of analytic initial data with a fixed radius of analyticity (Formula presented.), we show that the uniform radius of spatial analyticity (Formula presented.) of solutions at time (Formula presented.) cannot decay faster than (Formula presented.) as (Formula presented.). 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 ((Formula presented.), (Formula presented.)), where they obtained a decay rate of order (Formula presented.). Our proof relies on an approximate conservation law in a modified Gevrey spaces, local smoothing, and maximal function estimates.

approximate conservation law , decay rate , generalized KdV equation , higher order dispersion , modified Gevrey spaces , radius of spatial analyticity

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Department of Mathematics, Bahir Dar University, Bahir Dar, Ethiopia
Department of Mathematics, Nazarbayev University, Astana, Kazakhstan

Department of Mathematics
Department of Mathematics

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