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

Pietro Baldi

doi:10.3934/dcds.2006.15.883

Article Contents

2006, Volume 15, Issue 3: 883-903. Doi: 10.3934/dcds.2006.15.883

This issue Previous Article $Z^d$ Toeplitz arrays Next Article Dynamics of the degree six Landen transformation

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

Pietro Baldi^1,

1.
Sissa, via Beirut 2-4, 34014 Trieste

Received: January 2005

Revised: November 2005

Published: September 2006

Abstract Related Papers Cited by

Abstract

We consider 1D completely resonant nonlinear wave equations of the type $v_{t t}$ - $v_{x x}$$ = -v^3 + \mathcal{O}(v^4)$ 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.

Keywords:

Nonlinear wave equation,
inﬁnite dimensional Hamiltonian systems,
quasi-periodic solutions,
Lyapunov-Schmidt reduction.

Mathematics Subject Classification: 35L05, 35B15, 37K50.

Citation:

Article Metrics

HTML views() PDF downloads(102) Cited by(0)

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

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

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

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content