Discrete peakons

PHYSICA D-NONLINEAR PHENOMENA

卷:207

Article

Comech, A ; Cuevas, J ; Kevrekidis, PG

关键词: Klein-Gordon;    nonlinear Schrodinger;    discrete models;    long-range interactions;    peakons;    solitary waves;    stability analysis;   

DOI  :  10.1016/j.physd.2005.05.019

来源: Elsevier

【 摘 要 】

We demonstrate the possibility for explicit construction in a discrete Hamiltonian model of an exact solution of the form exp(-vertical bar n vertical bar), 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 Schrodinger-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. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

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