Quasi-periodic solutions for quasi-linear generalized KdV equations
| dc.contributor.advisor | ||
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Giuliani, Filippo | |
| dc.date.accessioned | 2016-07-12T10:50:32Z | |
| dc.date.available | 2016-07-12T10:50:32Z | |
| dc.date.issued | 2016-07 | |
| dc.description.abstract | We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The proof is based on an iterative Nash-Moser algorithm. To initialize this scheme, we need to perform a bifurcation analysis taking into account the strongly perturbative effects of the nonlinearity near the origin. In particular, we implement a weak version of the Birkhoff normal form method. The inversion of the linearized operators at each step of the iteration is achieved by pseudo-differential techniques, linear Birkhoff normal form algorithms and a linear KAM reducibility scheme. | en_US |
| dc.identifier.sissaPreprint | 38/2016/MATE | |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/35204 | |
| dc.language.iso | en | en_US |
| dc.miur.area | 1 | en_US |
| dc.publisher | SISSA | en_US |
| dc.relation.firstpage | 1 | en_US |
| dc.relation.lastpage | 62 | en_US |
| dc.subject | Quasi-linear Partial differential equations | en_US |
| dc.subject | Quasi-periodic solutions | en_US |
| dc.subject | Nash-Moser theory | en_US |
| dc.subject | KAM for PDE's | en_US |
| dc.subject.miur | MAT/05 | en_US |
| dc.title | Quasi-periodic solutions for quasi-linear generalized KdV equations | en_US |
| dc.type | Preprint | en_US |