Counter propagating two soliton solutions in the Fermi Pasta Ulam lattice
We study the interaction of small amplitude, long wavelength solitary waves in the Fermi Pasta Ulam model with general nearest neighbour 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 intermediate values of time these solutions describe the interaction of two counter propagating pulses. These solutions are stable with respect to perturbations in l2 and asymptotically stable with respect to perturbations which decay exponentially at spatial