Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices
Abstract
Here, we explore the possibility of multi-site breather states in a nonlinear Klein–Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this nonlinear instability is through the resonance with the wave continuum of a multiple of an internal mode eigenfrequency in the linearization of excited breather states. For the nonlinear instability, the internal mode must have its Krein signature opposite to that of the wave continuum. This mechanism is not only theoretically proposed, but also numerically corroborated through two concrete examples of the Klein–Gordon lattice with a soft (Morse) and a hard (Φ4) potential. Compared to the case of the nonlinear Schrödinger lattice, the Krein signature of the internal mode relative to that of the wave continuum may change depending on the period of the multi-site breather state. For the periods for which the Krein signatures of the internal mode and the wave continuum coincide, multi-site breather states are observed to be nonlinearly stable.
- Authors:
-
- Univ. de Sevilla, Sevilla (Spain)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
- McMaster Univ., Hamilton, ON (Canada); Nizhny Novgorod State Technical Univ., Novgorod (Russia)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1246360
- Report Number(s):
- LA-UR-15-22633
Journal ID: ISSN 0022-2526
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Studies in Applied Mathematics
- Additional Journal Information:
- Journal Volume: 6; Journal ID: ISSN 0022-2526
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Mathematics
Citation Formats
Cuevas-Maraver, Jesus, Kevrekidis, Panayotis G., and Pelinovsky, Dmitry E. Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices. United States: N. p., 2016.
Web. doi:10.1111/sapm.12107.
Cuevas-Maraver, Jesus, Kevrekidis, Panayotis G., & Pelinovsky, Dmitry E. Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices. United States. https://doi.org/10.1111/sapm.12107
Cuevas-Maraver, Jesus, Kevrekidis, Panayotis G., and Pelinovsky, Dmitry E. Mon .
"Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices". United States. https://doi.org/10.1111/sapm.12107. https://www.osti.gov/servlets/purl/1246360.
@article{osti_1246360,
title = {Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices},
author = {Cuevas-Maraver, Jesus and Kevrekidis, Panayotis G. and Pelinovsky, Dmitry E.},
abstractNote = {Here, we explore the possibility of multi-site breather states in a nonlinear Klein–Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this nonlinear instability is through the resonance with the wave continuum of a multiple of an internal mode eigenfrequency in the linearization of excited breather states. For the nonlinear instability, the internal mode must have its Krein signature opposite to that of the wave continuum. This mechanism is not only theoretically proposed, but also numerically corroborated through two concrete examples of the Klein–Gordon lattice with a soft (Morse) and a hard (Φ4) potential. Compared to the case of the nonlinear Schrödinger lattice, the Krein signature of the internal mode relative to that of the wave continuum may change depending on the period of the multi-site breather state. For the periods for which the Krein signatures of the internal mode and the wave continuum coincide, multi-site breather states are observed to be nonlinearly stable.},
doi = {10.1111/sapm.12107},
journal = {Studies in Applied Mathematics},
number = ,
volume = 6,
place = {United States},
year = {Mon Aug 01 00:00:00 EDT 2016},
month = {Mon Aug 01 00:00:00 EDT 2016}
}
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