The first part of the work has concluded that bending waves in a ring, being the low-frequency modes of resonant triplets, are stable against small perturbations. Consequently, on the one hand, a bending wave should behave as a linear quasi-harmonic wavetrain. The first-order approximation analysis predicts that the triple-mode interactions cannot play a primary role in the evolution of bending waves. On the other hand, one may anticipate that the intense bending wavetrain can be subject to the self-modulation during the long-time evolution. It means that these cannot be stable for a long time. This paper confirms such expectations, when exiting the framework of the first-order nonlinear analysis. To describe the nonlinear dynamics of the ring in detail, one should allow for higher-order approximation effects in a model. Such effects are associated with the concurrence between the diffusion of wave packets, because of different group velocities, and the amplitude-dependent dispersion of phase velocities, caused by the nonlinearity. Within the second-order approximation analysis, the amplitude modulation is experienced for intense bending waves. As a result, the soliton-like envelopes can be formed from unstable bending wavetrains.
1998, vol. 126, no1-4, pp. 201-212 (12 ref.)