Prof. Yair Zarmi

Several integrable evolution equations generate soliton approximations for complex dynamical systems. In these approximations, soliton interactions are confined to a finite collision region, and their collisions are elastic. The full solution of a system accounts for additional soliton interac-tions, corresponding to elastic and inelastic scattering.

Traditional analyses of such systems do not identify these scattering processes, nor do they ensure that soliton interactions remain localized. This results in cases, in which the perturbation series for the full solution of a system is not bounded order-by-order.

A new approach to the analysis of the full solution of such systems will be presented. It ensures that the local nature of soliton interactions is maintained in every order of the expansion, and all terms in the perturbation series for the solution are bounded. Pure elastic and inelastic soliton col-lisions are identified.

Both elastic and inelastic components in the full solution tend asymptotically to contributions of well-separated single solitons. In the elastic component, the solitons are unaffected by one an-other. Inelastic processes include soliton decay or merging, soliton-anti-soliton annihilation, dis-persive waves that decay away from soliton trajectories, and more.

Results of the new approach will be presented in the case of the ion acoustic wave equations of plasma physics.