A Mel'nikov approach to soliton-like solutions of systems of discretized nonlinear Schrödinger equations

Michael Kollmann, Tassos Bountis

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7 Citations (Scopus)


We investigate a class of N coupled discretized nonlinear Schrödinger equations of interacting chains in a nonlinear lattice, which, in the limit of zero coupling, become integrable Ablowitz-Ladik differential-difference equations. We study the existence of stationary localized excitations, in the form of soliton-like time-periodic states, by reducing the system to a perturbed 2N-dimensional symplectic map, whose homoclinic orbits are obtained by a recently developed Mel'nikov analysis. We find that, depending on the perturbation, homoclinic orbits can be accurately located from the simple zeros of a Mel'nikov vector and illustrate our results in the cases N = 2 and 3.

Original languageEnglish
Pages (from-to)397-406
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Issue number2-4
Publication statusPublished - Jan 1 1998


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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