1 0 Ju n 20 08 Counterpropagating two - soliton solutions in the FPU lattice

We study the interaction of small amplitude, long wavelength solitary waves in the Fermi-Pasta-Ulam model with general nearest-neighbor interaction potential. We establish global-in-time existence and stability of counter-propagating solitary wave solutions. These solutions are close to the linear superposition of two solitary waves for large positive and negative values of time; for intemediate values of time these solutions describe the interaction of two counterpropagating pulses. These solutions are stable with respect to perturbations in ℓ 2 and asymptotically stable with respect to perturbations which decay exponentially at spatial ±∞.