Publication Date

2005

Journal or Book Title

Physica D: Nonlinear Phenomena

Abstract

We demonstrate the possibility for explicit construction in a discrete Hamiltonian model of an exact solution of the form exp(−|n|), i.e., a discrete peakon. These discrete analogs of the well-known, continuum peakons of the Camassa–Holm equation [R. Camassa, D.D. Holm, Phys. Rev. Lett. 71 (1993) 1661] are found in a model different from the one for their continuum siblings and from that of earlier studies in the discrete setting [A.A. Ovchinnikov, S. Flach, Phys. Rev. Lett. 83 (1999) 248]. Namely, we observe discrete peakons in Klein–Gordon-type and nonlinear Schrödinger-type chains with long-range interactions. The interesting linear stability differences between these two chains are examined numerically and illustrated analytically. Additionally, inter-site centered peakons are also obtained in explicit form and their stability is studied. We also prove the global well-posedness for the discrete Klein–Gordon equation, show the instability of the peakon solution, and the possibility of a formation of a breathing peakon.

Comments

This is the pre-published version harvested from arXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVK-4GGWG51-1&_user=1516330&_coverDate=08%2F01%2F2005&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=a9f567690b3a1429a8636a8d9378f83c&searchtype=a

Pages

137-160

Volume

207

Issue

3-4

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