Solitons in Interaction

Several new nonlinear systems are given which are completely integrable. These systems can be considered as flows describing the self-interaction of single solitons in multisoliton fields. The construction of action variables, recursion operators, bi-hamiltonian formulation and the like is performed for these nonlinear systems. Furthermore virtual solitons are introduced and it is shown that 2-solitons in general may be understood as the superposition of two pairs of interacting solitons exchanging one virtual soliton and that the interacting soliton itself can be considered as the result of a collision of a wave with a virtual soliton. In a sense, virtual solitons only pop up during the time that solitons interact with each other. In case of the KdV the details of decomposition into interacting and virtual sQlitons are plotted, and a qualitative analysis of interaction is given. A brief discussion is appended, how to describe multisolitons by their "trajectories".