Numerical Studies of Localized Vibrating Structures in Nonlinear Lattices

A simple numerical model using a modified Euler's method was developed to model nonlinear lattices. This model was used to study the properties of four breather and kink type solitons in the cutoff modes of a lattice of linearly coupled oscillators with a cubic nonlinearity. These cutoff mode solitons were shown to correspond very well to the theoretical predictions of Larraza and Putterman 1984 and the experimental work of Denardo 1990. In addition, a fifth soliton was discovered in the upper cutoff mode, which was not anticipated by the theory. A preliminary analytical attempt to describe this soliton and to describe solitons in the intermediate modes, due to Larraza, Putterman, and the author, is presented. Additional numerical work on intermediate mode solitons and domain walls was performed. These studies showed that kink solitons are ubiquitous, and that they appear to be intimately linked to domain wall structures. In order to demonstrate the flexibility of the computer program developed, the model was extended to include two dimensional and lattices and one dimensional lattices with nonuniform characteristics. Two dimensional breather and kink solitons are described. Finally, a Toda lattice was modeled and some preliminary results obtained in preparation for future work.