Observations of Breather Solitons in a Nonlinear Vibratory Lattice

摘要

Experimental, numerical and analytical investigations of steady-state uppercutoff breather solitons in a one-dimensional lattice of coupled nonlinear oscillators are reported. These states are self-localized standing wave structures that can be considered as amplitude modulations of the upper cutoff mode, in which each oscillator is 180 deg out of phase with its immediate neighbors. The observation of the upper cutoff breather follows observations by previous investigators of three other types of cutoff silitons: lower cutoff breathers, and lower and upper cutoff kinks. The experimental system is a lattice of magnetically coupled pendulums that is oscillated vertically. Numerical simulations are made in a lattice that approximately models the actual lattice. The structures are analytically described by a solution to a nonlinear Schrodinger equation supplemented with zero and second harmonics. The harmonic terms produce an antisymmetry in the breather amplitude profile that is noticeable in the experimental data and can be extreme in the numerical simulations.