Discrete peakons
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) 1...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/24698 |
| Acesso em linha: | http://hdl.handle.net/11441/24698 https://doi.org/10.1016/j.physd.2005.05.019 |
| Access Level: | acceso abierto |
| Palavra-chave: | Klein–Gordon Nonlinear Schr ̈ odinger Discrete models Long-range interactions Peakons Solitary waves Stability analysis |
| Resumo: | 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. |
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