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A note on the Degasperis-Procesi equation. (English) Zbl 1067.35078
Summary: We prove that smooth solutions of the Degasperis-Procesi equation \[ u_t-u_{txx}+4uu_x=3u_xu_{xx}+uu_{xxx},\quad x \in\mathbb{R},\;t\geq 0, \] have infinite propagation speed: they loose instantly the property of having compact support.

MSC:
35Q35 PDEs in connection with fluid mechanics
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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