Soliton interactions in some semidiscrete integrable systems

Abstract

In this paper, soliton interactions in three semidiscrete integrable systems are studied. It will be shown that in some cases the solitary waves of the semidiscrete integrable systems can interact elastically, i.e., the shapes, the amplitudes, and the velocities of waves preserve after undergoing collision. However, soliton interactions in the semidiscrete integrable systems possess different properties from the continuous solitons, for example, the shorter waves can travel faster than the taller ones. We also find that two stable solitary waves can be destroyed after interaction, and the elastic properties of collisions between two solitary waves are sensitively dependent on the choices of some parameters in solution. We therefore conclude that soliton interactions in semidiscrete integrable systems are richer than the ones in continuous soliton systems.