Persistence of supersonic periodic solutions for chains with anharmonic interaction potentials between neighbours and next to nearest neighbours

Christine Venney, Johannes Zimmer

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2 Citations (Scopus)
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Abstract

We consider an infinite chain of particles with nearest neighbour (NN) and next to nearest neighbour (NNN) being coupled by nonlinear springs. To mimic the Lennard–Jones potential, the NN and NNN springs act against each other. We prove that in contrast to the NN interaction case, there are supersonic periodic solutions.
Original languageEnglish
Pages (from-to)503-518
Number of pages16
JournalDynamical Systems: An International Journal
Volume26
Issue number4
DOIs
Publication statusPublished - Dec 2011

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Lennard-Jones potential
Persistence
Nearest Neighbor
Periodic Solution
Interaction
Lennard-Jones Potential

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abstract = "We consider an infinite chain of particles with nearest neighbour (NN) and next to nearest neighbour (NNN) being coupled by nonlinear springs. To mimic the Lennard–Jones potential, the NN and NNN springs act against each other. We prove that in contrast to the NN interaction case, there are supersonic periodic solutions.",
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AB - We consider an infinite chain of particles with nearest neighbour (NN) and next to nearest neighbour (NNN) being coupled by nonlinear springs. To mimic the Lennard–Jones potential, the NN and NNN springs act against each other. We prove that in contrast to the NN interaction case, there are supersonic periodic solutions.

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