Solitary waves for nonconvex FPU lattices

Hartmut Schwetlick; Johannes Zimmer

doi:10.1007/s00332-005-0735-0

Solitary waves for nonconvex FPU lattices

Hartmut Schwetlick, Johannes Zimmer

University of Bath

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Solitary waves in a one-dimensional chain of atoms (qj) _j∈Z) are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated that the invariance of the equations allows one to transform a system with nonconvex potential energy density to the situation under consideration.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Journal of Nonlinear Science
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s00332-005-0735-0
State	Published - Feb 2007
Externally published	Yes

Keywords

discrete nonlinear elasticity
double well
lattice dynamics
nonconvex energy
solitary waves

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10.1007/s00332-005-0735-0

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abstract = "Solitary waves in a one-dimensional chain of atoms (qj) j∈Z) are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated that the invariance of the equations allows one to transform a system with nonconvex potential energy density to the situation under consideration.",

keywords = "discrete nonlinear elasticity, double well, lattice dynamics, nonconvex energy, solitary waves",

author = "Hartmut Schwetlick and Johannes Zimmer",

note = "Funding Information: Both authors acknowledge the support of the Max Planck Institute for Mathematics in the Sciences, where this work began. We are grateful for stimulating discussions with John Toland of the Department of Mathematical Sciences, University of Bath. J.Z. gratefully acknowledges the financial support of the Deutsche Forschungsgemeinschaft through an Emmy Noether grant (Zi 751/1-1) and the financial support of the EPSRC through an Advanced Research Fellowship (GR/S99037/1).",

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AU - Zimmer, Johannes

N1 - Funding Information: Both authors acknowledge the support of the Max Planck Institute for Mathematics in the Sciences, where this work began. We are grateful for stimulating discussions with John Toland of the Department of Mathematical Sciences, University of Bath. J.Z. gratefully acknowledges the financial support of the Deutsche Forschungsgemeinschaft through an Emmy Noether grant (Zi 751/1-1) and the financial support of the EPSRC through an Advanced Research Fellowship (GR/S99037/1).

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N2 - Solitary waves in a one-dimensional chain of atoms (qj) j∈Z) are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated that the invariance of the equations allows one to transform a system with nonconvex potential energy density to the situation under consideration.

AB - Solitary waves in a one-dimensional chain of atoms (qj) j∈Z) are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated that the invariance of the equations allows one to transform a system with nonconvex potential energy density to the situation under consideration.

KW - discrete nonlinear elasticity

KW - double well

KW - lattice dynamics

KW - nonconvex energy

KW - solitary waves

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JO - Journal of Nonlinear Science

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Solitary waves for nonconvex FPU lattices

Abstract

Keywords

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