# American Institute of Mathematical Sciences

doi: 10.3934/dcds.2020312

## Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity

 1 Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d'Orsay, 91405 Orsay, France 2 School of Mathematics and Statistics, Lanzhou University, 370000 Lanzhou, China

* Corresponding author

Received  April 2020 Revised  July 2020 Published  August 2020

Fund Project: The work of both authors was partially supported by the ANR project ANuI (ANR-17-CE40-0035-02)

We prove global existence and modified scattering for the solutions of the Cauchy problem to the fractional Korteweg-de Vries equation with cubic nonlinearity for small, smooth and localized initial data.

Citation: Jean-Claude Saut, Yuexun Wang. Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity. Discrete & Continuous Dynamical Systems - A, doi: 10.3934/dcds.2020312
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