Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site

Peter Jason and Magnus Johansson
Phys. Rev. E 93, 012219 – Published 29 January 2016

Abstract

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

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  • Received 2 July 2015
  • Revised 14 October 2015

DOI:https://doi.org/10.1103/PhysRevE.93.012219

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Nonlinear Dynamics

Authors & Affiliations

Peter Jason* and Magnus Johansson

  • Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden

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Issue

Vol. 93, Iss. 1 — January 2016

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