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Quotidiano di informazione – Anno 30 n° 340

Posts Tagged ‘equations’

Quasi-periodic solutions for quasilinear generalized KdV equations

Posted by fidest press agency su lunedì, 17 ottobre 2016

algoritmoRoma Martedì 18 Ottobre 2016, ore 16:00 Dipartimento di Matematica e Fisica, Aula 211 Largo San L. Murialdo,1 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.Filippo Giuliani, SISSA, Trieste

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