Solitary waves on Fermi-Pasta-Ulam lattices: IV. Proof of stability at low energy

G. Friesecke; R. L. Pego

doi:10.1088/0951-7715/17/1/014

Solitary waves on Fermi-Pasta-Ulam lattices: IV. Proof of stability at low energy

G. Friesecke
, R. L. Pego

University of Warwick
University of Maryland, College Park

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

88 Scopus citations

Abstract

We establish the long-time stability of low-energy solitary waves in one-dimensional nonintegrable lattices with Hamiltonian H = Σ _j∈ℤ (1/2p_j² + V (q_j+1 - q_j)) with a general nearest-neighbour potential V. As a corollary we obtain a recurrence theorem related to numerical observations by Fermi, Pasta and Ulam.

Original language	English
Pages (from-to)	229-251
Number of pages	23
Journal	Nonlinearity
Volume	17
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/17/1/014
State	Published - Jan 2004
Externally published	Yes

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title = "Solitary waves on Fermi-Pasta-Ulam lattices: IV. Proof of stability at low energy",

abstract = "We establish the long-time stability of low-energy solitary waves in one-dimensional nonintegrable lattices with Hamiltonian H = Σ j∈ℤ (1/2pj2 + V (qj+1 - qj)) with a general nearest-neighbour potential V. As a corollary we obtain a recurrence theorem related to numerical observations by Fermi, Pasta and Ulam.",

author = "G. Friesecke and Pego, \{R. L.\}",

year = "2004",

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AU - Friesecke, G.

AU - Pego, R. L.

PY - 2004/1

Y1 - 2004/1

N2 - We establish the long-time stability of low-energy solitary waves in one-dimensional nonintegrable lattices with Hamiltonian H = Σ j∈ℤ (1/2pj2 + V (qj+1 - qj)) with a general nearest-neighbour potential V. As a corollary we obtain a recurrence theorem related to numerical observations by Fermi, Pasta and Ulam.

AB - We establish the long-time stability of low-energy solitary waves in one-dimensional nonintegrable lattices with Hamiltonian H = Σ j∈ℤ (1/2pj2 + V (qj+1 - qj)) with a general nearest-neighbour potential V. As a corollary we obtain a recurrence theorem related to numerical observations by Fermi, Pasta and Ulam.

UR - https://www.scopus.com/pages/publications/0346671222

U2 - 10.1088/0951-7715/17/1/014

DO - 10.1088/0951-7715/17/1/014

M3 - Article

AN - SCOPUS:0346671222

SN - 0951-7715

VL - 17

SP - 229

EP - 251

JO - Nonlinearity

JF - Nonlinearity

IS - 1

ER -

Solitary waves on Fermi-Pasta-Ulam lattices: IV. Proof of stability at low energy

Abstract

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