[CvGmt News] Seminario di Filippo Giuliani (22/5/2018 ore 14:00 - Si noti il cambio di orario)

[Alfonso Sorrentino]

SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Universita' degli Studi di Roma "Tor Vergata"


(Si noti il cambio di orario)


Martedi' 22 Maggio 2018, ore 14:00 Aula Dal Passo


Filippo Giuliani (Universita' degli Studi "Roma Tre")


Titolo: On the integrability and quasi-periodic dynamics of the dispersive
Degasperis-Procesi equation


Abstract:  The Degasperis-Procesi equation

$$ u_t + c_0 u_x + gamma u_{xxx} -alpha^2 u_{xxt} = left( c_2
(u^2_x+uu_{xx}) - frac{2c_3}{alpha^2}u^2 ight)_x $$

has been extensively studied by many authors, especially in its
dispersionless form, since it presents interesting phenomena such as
breaking waves and existence of peakon-like solutions.
Degasperis-Holm-Hone proved the integrability of this equation and they
provided an iterative method to compute infinite conserved quantities.
Since the Degasperis-Procesi equation is a quasi-linear equation the
presence of dispersive terms depends on the chosen frame. In absence of
dispersive terms there are no constants of motion even controlling the
$H^1$-norm.
We show that, in the dispersive case, we can construct infinitely many
constants of motion which are analytic and control the Sobolev norms in a
neighborhood of the origin. Moreover, thanks to the analysis of the
algebraic structure of the quadratic parts of these conserved quantities we
show that the (formal) Birkhoff normal form is action-preserving
(integrable) at any order. This fact is used to prove the first existence
result of quasi-periodic solutions for the Degasperis-Procesi equation on
the circle.
These results have been obtained in collaboration with R. Feola, S.
Pasquali and M. Procesi.



Website: http://www.mat.uniroma2.it/~sorrenti/SeminarioED.html



-- 
Dipartimento di Matematica
Università degli Studi di Roma "Tor Vergata"
Via della Ricerca Scientifica 1
00133 Rome (Italy)

Phone: +39 06 72594663
Fax:      +39 06 72594699
Web page: http://www.mat.uniroma2.it/~sorrenti
Email: sorrentino at mat.uniroma2.it
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://cvgmt.sns.it/pipermail/news/attachments/20180515/26858a51/attachment.html>