Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain
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 po...
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| Format: | Article |
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Elsevier
2007
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| Online Access: | https://eprints.nottingham.ac.uk/925/ |
| _version_ | 1848790503736213504 |
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| author | Butt, Imran A. Wattis, Jonathan A.D. |
| author_facet | Butt, Imran A. Wattis, Jonathan A.D. |
| author_sort | Butt, Imran A. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:13:39Z |
| format | Article |
| id | nottingham-925 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:13:39Z |
| publishDate | 2007 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-9252020-05-04T20:28:42Z https://eprints.nottingham.ac.uk/925/ Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain Butt, Imran A. Wattis, Jonathan A.D. 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. Elsevier 2007 Article PeerReviewed 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. breathers non-linear waves discrete systems |
| spellingShingle | breathers non-linear waves discrete systems Butt, Imran A. Wattis, Jonathan A.D. Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain |
| title | Asymptotic analysis of combined breather-kink modes
in a Fermi-Pasta-Ulam chain |
| title_full | Asymptotic analysis of combined breather-kink modes
in a Fermi-Pasta-Ulam chain |
| title_fullStr | Asymptotic analysis of combined breather-kink modes
in a Fermi-Pasta-Ulam chain |
| title_full_unstemmed | Asymptotic analysis of combined breather-kink modes
in a Fermi-Pasta-Ulam chain |
| title_short | Asymptotic analysis of combined breather-kink modes
in a Fermi-Pasta-Ulam chain |
| title_sort | asymptotic analysis of combined breather-kink modes
in a fermi-pasta-ulam chain |
| topic | breathers non-linear waves discrete systems |
| url | https://eprints.nottingham.ac.uk/925/ |