@article {GIULIANI20175052,
	title = {Quasi-periodic solutions for quasi-linear generalized KdV equations},
	journal = {Journal of Differential Equations},
	volume = {262},
	number = {10},
	year = {2017},
	pages = {5052 - 5132},
	abstract = {<p>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{\textendash}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.</p>},
	keywords = {KAM for PDE{\textquoteright}s, KdV, Nash{\textendash}Moser theory, Quasi-linear PDE{\textquoteright}s, Quasi-periodic solutions},
	issn = {0022-0396},
	doi = {https://doi.org/10.1016/j.jde.2017.01.021},
	url = {http://www.sciencedirect.com/science/article/pii/S0022039617300487},
	author = {Filippo Giuliani}
}
