Quasi-periodic solutions of nonlinear wave equations with a prescribed potential

Xiaoping Yuan

doi:10.3934/dcds.2006.16.615

Article Contents

2006, Volume 16, Issue 3: 615-634. Doi: 10.3934/dcds.2006.16.615

This issue Previous Article Minimum 'energy' approximations of invariant measures for nonsingular transformations Next Article On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition

Quasi-periodic solutions of nonlinear wave equations with a prescribed potential

Xiaoping Yuan^1,

1.
School of Mathematical Sciences, Fudan University, Shanghai 200433

Received: October 31, 2005

Revised: June 30, 2006

Published: August 2006

Abstract Related Papers Cited by

Abstract

It is proved that for a prescribed potential $V$ there are many quasi-periodic solutions of nonlinear wave equations $u_{t t}-u_{x x}+V(x)u\pm u^3+O(|u|^5)=0$ subject to Dirichlet boundary conditions.

Keywords:

nonlinear wave equation,
KAM theorem,
infinite dimensional Hamiltonian systems,
quasi-periodic solutions.

Mathematics Subject Classification: 35L05, 37K55, 37C55.

Citation:

Article Metrics

HTML views() PDF downloads(85) Cited by(0)

Quasi-periodic solutions of nonlinear wave equations with a prescribed potential

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Quasi-periodic solutions of nonlinear wave equations with a prescribed potential

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content