01350nas a2200193 4500008004100000022001400041245007200055210006900127300001600196490000800212520074100220653001800961653000800979653002400987653002301011653002901034100002201063856007101085 2017 eng d a0022-039600aQuasi-periodic solutions for quasi-linear generalized KdV equations0 aQuasiperiodic solutions for quasilinear generalized KdV equation a5052 - 51320 v2623 a
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.
10aKAM for PDE's10aKdV10aNash–Moser theory10aQuasi-linear PDE's10aQuasi-periodic solutions1 aGiuliani, Filippo uhttp://www.sciencedirect.com/science/article/pii/S0022039617300487