A numerical study of large amplitude motion on a chain of coupled nonlinear oscillators

We have studied the behavior of large amplitude compressive displacements on one-dimensional lattices of equal masses which interact with a variety of nearest neighbor potential energy functions. For the cases of cyclic and fixed end boundary conditions solitons are found to exist and to completely determine the dynamics. The shapes of the solitons on the several lattices are remarkably alike, and all are very close to the shape of a Toda lattice soliton. Because reflection at a free end creates a dilational displacement, a solitary wave does not survive on a lattice with free ends. Mass inhomogeneities in the lattice also scatter solitary waves and lead to their destruction, but the rate of the process depends on the defect to host mass ratio. When that mass ratio is 13/12 a solitary wave survives at least 500 collisions, and its energy is modulated cyclically. The rate of destruction increases as the defect to host mass ratio increases. The results of the calculations are discussed with respect to the ubiquity of solitary wave behavior, its relation with the shape of the potential energy curve, and the possible role of metastable solitary pulses in intramolecular energy transfer.