Breather continuation from infinity in nonlinear oscillator chains

Guillaume James (1) , Dmitry E. Pelinovsky (2)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 Department of Mathematics and Statistics [Hamilton]

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. 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.

Mots clés: Discrete Klein--Gordon equation; discrete breathers; nonlocal bifurcations; asymptotic methods; fixed-point arguments

Domaines: Systèmes dynamiques [math.DS]

Guillaume James, Dmitry E. Pelinovsky. Breather continuation from infinity in nonlinear oscillator chains. Discrete and Continuous Dynamical Systems - Series A, 2012, 32 (5), pp.1775-1799. ⟨10.3934/dcds.2012.32.1775⟩. ⟨hal-00765684⟩