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 counterpropagating 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 2 and asymptotically stable with respect to perturbations which decay exponentially at spatial ±∞. Mathematics Subject Classification: 37K40, 37K60