Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices

Cuevas-Maraver, Jesus; Kevrekidis, Panayotis G.; Pelinovsky, Dmitry E.

doi:10.1111/sapm.12107

Title: Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices

Journal Article · Mon Aug 01 00:00:00 EDT 2016 · Studies in Applied Mathematics

DOI:https://doi.org/10.1111/sapm.12107· OSTI ID:1246360

Cuevas-Maraver, Jesus ^[1]; Kevrekidis, Panayotis G. ^[2]; Pelinovsky, Dmitry E. ^[3]

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)

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.

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Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1246360

Report Number(s):: LA-UR-15-22633

Journal Information:: Studies in Applied Mathematics, Vol. 6; ISSN 0022-2526

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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