G Friesecke and R L Pego 2004 Nonlinearity 17 229 doi:10.1088/0951-7715/17/1/014
Solitary waves on Fermi–Pasta–Ulam lattices: IV. Proof of stability at low energy
G Friesecke1 and R L Pego2
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We establish the long-time stability of low-energy solitary waves in one-dimensional nonintegrable lattices with Hamiltonian ![\[ \begin{eqnarray*}H = \sum_{j\in {\Bbb Z}} \left(\frac{1}{2} p_j^2 + V(q_{j+1}-q_j)\right)\end{eqnarray*} \]](http://ej.iop.org/images/0951-7715/17/1/014/non163384ude001.gif)
with a general nearest-neighbour potential V. As a corollary we obtain a recurrence theorem related to numerical observations by Fermi, Pasta and Ulam.
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Issue 1 (January 2004)
Received 12 May 2003, in final form 13 May 2003
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Solitary waves on Fermi–Pasta–Ulam lattices: IV. Proof of stability at low energy
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