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

Butt, Imran A. and Wattis, Jonathan A.D. (2007) Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain. Physica D, 231 . pp. 165-179.

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We find approximations to travelling breather solutions of the

one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright

breather and dark breather solutions are found. We find that the

existence of localised (bright) solutions depends upon the

coefficients of cubic and quartic terms of the potential energy,

generalising an earlier inequality derived by James [CR Acad Sci

Paris 332, 581, (2001)]. We use the method of multiple scales to

reduce the equations of motion for the lattice to a nonlinear

Schr{\"o}dinger equation at leading order and hence construct an

asymptotic form for the breather. We show that in the absence of

a cubic potential energy term, the lattice supports combined

breathing-kink waveforms. The amplitude of breathing-kinks can be

arbitrarily small, as opposed to traditional monotone kinks, which

have a nonzero minimum amplitude in such systems. We also present

numerical simulations of the lattice, verifying the shape and

velocity of the travelling waveforms, and confirming the

long-lived nature of all such modes.

Item Type: Article
Keywords: breathers, non-linear waves, discrete systems
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Depositing User: Wattis, Jonathan
Date Deposited: 23 Jul 2008 14:30
Last Modified: 04 May 2020 20:28

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