Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9877590 | Physica D: Nonlinear Phenomena | 2005 | 24 Pages |
Abstract
We demonstrate the possibility for explicit construction in a discrete Hamiltonian model of an exact solution of the form expâ¡(â|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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
A. Comech, J. Cuevas, P.G. Kevrekidis,