Counterpropagating Two-Soliton Solutions in the FPU Lattice

Details Counterpropagating Two-Soliton Solutions in the FPU Lattice Counterpropagating Two-Soliton Solutions in the FPU Lattice

2008-06-10

arxiv.org/abs/0806.1637v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

10.1088/0951-7715/21/12/011

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 $\ell^2$ and asymptotically stable with respect to perturbations which decay exponentially at spatial $\pm \infty$.}

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