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Title: 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 (Φ 4) 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:
 [1];  [2];  [3]
  1. Univ. de Sevilla, Sevilla (Spain)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
  3. 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:
Journal Article: 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. doi:10.1111/sapm.12107.
Cuevas-Maraver, Jesus, Kevrekidis, Panayotis G., and Pelinovsky, Dmitry E. 2016. "Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices". United States. doi: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 = 2016,
month = 8
}

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