Numerical investigations of breather solitons in nonlinear vibratory lattices
Walden, Cleon A.
Denardo, Bruce C.
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Breather solitons in a one-dimensional lattice of coupled nonlinear oscillators are numerically investigated. These are localized nonpropagating steady states that exist at frequencies either below the linear cutoff frequency (corresponding to the extended mode in which all the oscillators are in-phase) or above the upper linear cutoff frequency (corresponding to the extended mode in which each oscillator is 180° out-of-phase with its immediate neighbors). The lattice is damped and parametrically driven. A nonlinear Schrodinger theory, which assumes a modulational amplitude that is weakly nonlinear and slowly varying in space, is compared to the numerical data. The error is roughly 5% at low amplitudes and 20% at high amplitudes. The regions in the drive parameter plane (amplitude vs frequency) where the breathers exist are numerically determined and compared to theory. A substantial discrepancy occurs at lower drive amplitudes where the theory predicts that the lower cutoff breather should exist, but where an instability is observed. Also in contrast to the theory, the region of the upper cutoff breather has relatively large areas in which quasiperiodicity occurs or the motion decays to rest. Quasiperiodicity is also observed in the lower cutoff breather. Finally, instead of a global parametric drive, an end drive is investigated. It is found that, for drive frequencies outside the linear propagation band, there is an amplitude threshold for the periodic ejection or "shedding" of propagating breather solitons. The quasiperiodicity that occurs for a global parametric drive may be a consequence of soliton shedding.
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