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Quasi-periodic solutions for quasi-linear generalized KdV equations

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dc.contributor.advisor Giuliani, Filippo 2016-07-12T10:50:32Z 2016-07-12T10:50:32Z 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.language.iso en en_US
dc.publisher SISSA 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.title Quasi-periodic solutions for quasi-linear generalized KdV equations en_US
dc.type Preprint en_US
dc.subject.miur MAT/05 en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.identifier.sissaPreprint 38/2016/MATE
dc.relation.firstpage 1 en_US
dc.relation.lastpage 62 en_US

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