On the integrability of Degasperis–Procesi equation: Control of the Sobolev norms and Birkhoff resonances

@article{Feola2019OnTI,
  title={On the integrability of Degasperis–Procesi equation: Control of the Sobolev norms and Birkhoff resonances},
  author={Roberto Feola and Filippo Giuliani and Stefano Pasquali},
  journal={Journal of Differential Equations},
  year={2019}
}
We consider the dispersive Degasperis-Procesi equation $u_t-u_{x x t}-\mathtt{c} u_{xxx}+4 \mathtt{c} u_x-u u_{xxx}-3 u_x u_{xx}+4 u u_x=0$ with $\mathtt{c}\neq 0$. In \cite{Deg} the authors proved that this equation possesses infinitely many conserved quantities. We prove that, in a neighborhood of the origin, there are infinitely many of such constants of motion which control the Sobolev norms and which are analytic in a neighborhood of the origin of some $H^s$ Sobolev space, both on $\mathbb… Expand
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