Effective Hamiltonian for traveling discrete breathers in the FPU chain

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August 2005, 5(3): 719-734. doi: 10.3934/dcdsb.2005.5.719

Effective Hamiltonian for traveling discrete breathers in the FPU chain

Michael Kastner ^1, and Jacques-Alexandre Sepulchre ^2,

1.	Physikalisches Institut, Theoretische Physik I, Universität Bayreuth, 95440 Bayreuth, Germany
2.	Institut Non Linéaire de Nice, 1361 Route des Lucioles, 06560 Sophia Antipolis, France

Received September 2003 Revised October 2004 Published May 2005

Abstract
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For the Fermi-Pasta-Ulam chain, an effective Hamiltonian is constructed, describing the motion of approximate, weakly localized discrete breathers traveling along the chain. The velocity of these moving and localized vibrations can be estimated analytically as the group velocity of the corresponding wave packet. The Peierls-Nabarro barrier is estimated for strongly localized discrete breathers.

Keywords: Fermi-Pasta-Ulam chain, traveling discrete breathers, Peierls-Nabarro potential., effective Hamiltonian.

Mathematics Subject Classification: 34C15, 37K05, 37K60, 70K7.

Citation: Michael Kastner, Jacques-Alexandre Sepulchre. Effective Hamiltonian for traveling discrete breathers in the FPU chain. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 719-734. doi: 10.3934/dcdsb.2005.5.719

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