Energy exchange in collisions of intrinsic localized modes

Energy transfer process is examined numerically for the binary collision of intrinsic localized modes (ILMs) in the Fermi-Pasta-Ulam beta lattice. Unlike "solitons" in the integrable systems, ILMs exchange their energy in collision due to the discreteness effect. The mechanism of this energy exchange is examined in detail, and it is shown that the phase difference is the most dominant factor in the energy exchange process and, generally speaking, the ILM with advanced phase absorbs energy from the other. Heuristic model equations which describe the energy transfer of ILMs are proposed by considering the ILMs as interacting "particles." The results due to these equations agree qualitatively very well with those of the numerical simulations. In some cases, the relation between the phase difference of the ILMs and the transferred energy becomes singular, which may be regarded as one of the major mechanisms responsible for the generation of "chaotic breathers."