G. James and D. Pelinovsky
Breather continuation from infinity in
nonlinear oscillator chains
Discrete and Continuous Dynamical Systems A 32, 1775-1799 (2012)
Abstract:
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.
Keywords:
Discrete Klein-Gordon equation, discrete breathers, nonlocal bifurcations,
asymptotic methods, fixed-point arguments.