Instability and confined chaos in a nonlinear dispersive wave system

Calculations of a discrete nonlinear dispersive wave system show that as the degree of nonlinearity increases, the system experiences in turn, periodic, recurring, chaotic, transitional, and periodic motions. A relationship between the instability of the initial configuration and the long-time behavior is identified. The calculations further suggest that the corresponding continuous system will exhibit chaotic motions and energy-sharing among a narrow band of unstable modes, a phenomenon which we call ‘‘confined chaos.’’