Chaos and localization in the discrete nonlinear Schrödinger equation

Stefano Iubini and Antonio Politi

Chaos, Solitons & Fractals, 2021, vol. 147, issue C

Abstract: We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schrödinger equation. This nonintegrable model, ubiquitous in several fields of physics, describes the behavior of an array of coupled complex oscillators with a local nonlinear potential. We explore the Lyapunov spectrum for different values of the energy density, finding that the maximal value of the Kolmogorov-Sinai entropy is attained at infinite temperatures. Moreover, we revisit the dynamical freezing of relaxation to equilibrium, occurring when large localized states (discrete breathers) are superposed to a generic finite-temperature background. We show that the localized excitations induce a number of very small, yet not vanishing, Lyapunov exponents, which signal the presence of extremely long characteristic time-scales. We widen our analysis by computing the related Lyapunov covariant vectors, to investigate the interaction of a single breather with the various degrees of freedom.

Keywords: Discrete nonlinear Schrödinger equation; Discrete breathers; Lyapunov spectrum; Lyapunov covariant vectors (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003088

DOI: 10.1016/j.chaos.2021.110954

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