Quasi-periodic solutions of the equation $v_{t t} - v_{x x} +v^3 = f(v)$ | Zendy

Pietro Baldi | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Quasi-periodic solutions of the equation $v_{t t} - v_{x x} +v^3 = f(v)$

Author(s) -

Pietro Baldi

Publication year - 2006

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2006.15.883

Subject(s) - physics , superposition principle , order (exchange) , periodic wave , amplitude , type (biology) , nonlinear system , mathematical analysis , periodic boundary conditions , modulation (music) , boundary value problem , mathematical physics , traveling wave , mathematics , quantum mechanics , ecology , finance , acoustics , economics , biology

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

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research