GEOMETRICALLY INDUCED NONLINEAR DYNAMICS IN ONE-DIMENSIONAL LATTICES

We present a simple lattice model consisting of a chain of coupled oscillators, where their masses are interconnected by linear springs and allowed to move along a common axis, as in a monorail. In the transverse direction each mass is also attached to two other springs, one on each side of the mass. The ends of these springs are kept at fixed positions. The nonlinearity in the model arises from the geometric constraints imposed on the motion of the masses, as well as from the configuration of the springs, where in the transverse directions the springs are either in the extended or compressed state depending on the position of the mass. Under these conditions we show that solitary waves (domain walls) are present in the system. In the long wavelength limit an analytical solution for these nonlinear waves is found. Numerical integrations of the equations of motion in the full discrete system are also performed to analyze the stability of the domain wall solution. Nonlinear supratransmission is also shown to exist in the model and a discussion of mechanism is presented.