BREATHER SELF-TRAPPING AND DELOCALIZATION IN 2D SYSTEM OF WEAKLY COUPLED NONLINEAR CHAINS
Alexander Savin, Leonid Manevitch
We present analytical and numerical studies of nonlinear localized
short-wavelength excitations (breathers) in a system of two weakly
coupled chains of nonlinear oscillators, which in particular can
model dynamics of weakly coupled polymer chains in polymer
crystals. Periodic transverse translation (wandering) of
low-amplitude breather in a system of several, up to five, coupled
nonlinear chains is described, and the dependence of the wandering
period on the number of chains is analytically estimated and
compared with numerical results. On-chain self-trapping of
large-amplitude 1D breather and delocalization of the breather in
2D system of a large number of coupled nonlinear chains is
described, in which the breather, initially excited in a given 1D
chain, abruptly spreads its vibrational energy in the whole 2D
system upon decreasing breather frequency or amplitude below the
threshold one. The threshold breather frequency is above the cut
off phonon frequency in 2D system, and the threshold breather
amplitude scales as square root of the inter-chain coupling
constant. Such delocalizing transition of discrete breather in 2D
and 3D system of coupled nonlinear chains also has an analogy with
delocalizing transition of Bose-Einstein condensates in 2D and 3D
optical lattices. The analytical results are confirmed by computer
simulations.