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Asymptotic analysis of combined breather-kink modes\ud in a Fermi-Pasta-Ulam chain

By Imran A. Butt and Jonathan A.D. Wattis

Abstract

We find approximations to travelling breather solutions of the\ud one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright\ud breather and dark breather solutions are found. We find that the\ud existence of localised (bright) solutions depends upon the\ud coefficients of cubic and quartic terms of the potential energy,\ud generalising an earlier inequality derived by James [CR Acad Sci\ud Paris 332, 581, (2001)]. We use the method of multiple scales to\ud reduce the equations of motion for the lattice to a nonlinear\ud Schr{\"o}dinger equation at leading order and hence construct an\ud asymptotic form for the breather. We show that in the absence of\ud a cubic potential energy term, the lattice supports combined\ud breathing-kink waveforms. The amplitude of breathing-kinks can be\ud arbitrarily small, as opposed to traditional monotone kinks, which\ud have a nonzero minimum amplitude in such systems. We also present\ud numerical simulations of the lattice, verifying the shape and\ud velocity of the travelling waveforms, and confirming the\ud long-lived nature of all such modes

Publisher: Elsevier
OAI identifier: oai:eprints.nottingham.ac.uk:925
Provided by: Nottingham ePrints

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