Breather continuation from infinity in nonlinear oscillator chains

Guillaume James, Dmitry Pelinovsky
2012 Discrete and Continuous Dynamical Systems. Series A  
Existence of large-amplitude time-periodic breathers localized near a single site is proved for the discrete Klein-Gordon equation, in the case when the derivative of the on-site potential has a compact support. Breathers are obtained at small coupling between oscillators and under nonresonance conditions. Our method is different from the classical anti-continuum limit developed by MacKay and Aubry, and yields in general branches of breather solutions that cannot be captured with this approach.
more » ... When the coupling constant goes to zero, the amplitude and period of oscillations at the excited site go to infinity. Our method is based on near-identity transformations, analysis of singular limits in nonlinear oscillator equations, and fixed-point arguments.
doi:10.3934/dcds.2012.32.1775 fatcat:57psrjtpufhhnnkdxvga25zh5y