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Chaos and localization in the discrete nonlinear Schrödinger equation

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  • Iubini, Stefano
  • Politi, Antonio

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.

Suggested Citation

  • Iubini, Stefano & Politi, Antonio, 2021. "Chaos and localization in the discrete nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003088
    DOI: 10.1016/j.chaos.2021.110954
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    References listed on IDEAS

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    1. Trombettoni, A. & Nistazakis, H.E. & Rapti, Z. & Frantzeskakis, D.J. & Kevrekidis, P.G., 2009. "Soliton dynamics in linearly coupled discrete nonlinear Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(4), pages 814-824.
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