NSC Seminar Interactions of localized coherent structures in nonintegrable dispersive systems

2007-07-26 14:00 - 2007-07-26 15:30
Dr.Baofeng Feng
Pulse solutions occur in various physical systems: surface waves in shallow waters, plasma waves, optical solitons and intrinsic localized modes in nonlinear lattices. In spite of this diversity, interactions between these pulses share a common feature, that is, the collision usually results in energy exchange, whose amount depends crucially on the phase difference at the moment of collision. In the first part of my talk, I will give a brief review on the interactions between pulses in different physical systems with a particular focus on the nonlinear optics. In the second part, the energy exchange for the collision of intrinsic localized modes in Fermi-Pasta-Ulam (FPU) lattice will be theoretically explored. First, a regularized PDE model is derived to describe intrinsic localized modes in FPU lattice. Then, a simplified ODE model is further derived based on the modified conservation laws. The results of direct simulations for the energy exchange from the ODE model with the ones in FPU lattices. Finally, we believe that a universal energy exchange mechanism holds behind the diverse dispersive systems.