Quasi-periodic solutions of the equation v_tt-v_xx+v³=f(v)

2005/06/05 by Pietro Baldi, Baldi, Pietro
Mathematics · #35B15 #35L05 #37K50 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B15 #msc:35L05 #msc:37K50

paper · pdf · doi:10.48550/arxiv.math/0506089

20 pages. Corrected some misprints, added a reference, moved Proposition and Lemma 1 from Section 2 to the Appendix

arxiv created 2005/07/06 · arxiv updated 2009/12/01

Abstract

We consider 1D completely resonant nonlinear wave equations of the type v_tt-v_xx=-v³+O(v⁴) with spatial periodic boundary conditions. We prove the existence of a new type of quasi-periodic small amplitude solutions with two frequencies, for more general nonlinearities. These solutions turn out to be, at the first order, the superposition of a traveling wave and a modulation of long period, depending only on time.

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