We consider 1D completely resonant nonlinear wave equations of the type vtt - vxx = -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.
Quasi-periodic solutions of the equation v_tt - v_xx + v^3 = f(v) / Baldi, Pietro. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 15:3(2006), pp. 883-903. [10.3934/dcds.2006.15.883]
Quasi-periodic solutions of the equation v_tt - v_xx + v^3 = f(v)
BALDI, PIETRO
2006
Abstract
We consider 1D completely resonant nonlinear wave equations of the type vtt - vxx = -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.File in questo prodotto:
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