Characterization of soliton solutions in 2D nonlinear Schrödinger lattices by using the spatial disorder

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Abstract

In this paper, the pattern of the soliton solutions to the discrete nonlinear Schrödinger (DNLS) equations in a 2. D lattice is studied by the construction of horseshoes in l∞-spaces. The spatial disorder of the DNLS equations is the result of the strong amplitudes and stiffness of the nonlinearities. The complexity of this disorder is log(N+1) where N is the number of turning points of the nonlinearities. For the case N=1, there exist disjoint intervals I0 and I1, for which the state um,n at site (m,n) can be either dark (um,n∈I0) or bright (um,n∈I1) that depends on the configuration km,n=0 or 1, respectively. Bright soliton solutions of the DNLS equations with a cubic nonlinearity are also discussed.

Original languageEnglish
Pages (from-to)736-749
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume415
Issue number2
DOIs
Publication statusPublished - 2014 Jul 15

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Keywords

  • Bright solitons
  • Discrete nonlinear schrödinger equation
  • Horseshoe
  • Soliton solution
  • Spatial disorder

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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