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On the persistence of spatial analyticity for generalized KdV equation with higher order dispersion
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AbstractPersistence of spatial analyticity is studied for solutions of the generalized Korteweg‐de Vries (KdV) equation with higher order dispersionwhere , 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.
Title: On the persistence of spatial analyticity for generalized KdV equation with higher order dispersion
Description:
AbstractPersistence of spatial analyticity is studied for solutions of the generalized Korteweg‐de Vries (KdV) equation with higher order dispersionwhere , 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.
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