Quasi-periodic solutions for quasi-linear generalized KdV equations
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.
Cite
@article{arxiv.1607.02583,
title = {Quasi-periodic solutions for quasi-linear generalized KdV equations},
author = {Filippo Giuliani},
journal= {arXiv preprint arXiv:1607.02583},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1404.3125, arXiv:1508.02007, arXiv:1602.02411 by other authors