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Keywords:
higher order nonlinear dispersive equation; radius of spatial analyticity; approximate conservation law
higher order nonlinear dispersive equation; radius of spatial analyticity; approximate conservation law
Summary:
In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data $u_{0}$. The analytic initial data can be extended as holomorphic functions in a strip around the $x$-axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
References:
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