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Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne

Aaron Hoffman

We study the interaction of small amplitude, long-wavelength solitary wavesin the Fermi–Pasta–Ulam model with general nearest-neighbour interactionpotential. We establish global-in-time existence and stability of counterpropagatingsolitary wave solutions. These solutions are close to the linearsuperposition of two solitary waves for large positive and negative values oftime; for intermediate values of time these solutions describe the interactionof two counter-propagating pulses. These solutions are stable with respectto perturbations in L2 and asymptotically stable with respect to perturbationswhich decay exponentially at spatial ±∞.