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One- and two-dimensional solitons in second-harmonic-generating lattices.

Boris A Malomed1, P G Kevrekidis, D J Frantzeskakis

  • 1Department of Inderdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
Summary

This study explores solitary-wave solutions in dynamical lattices, identifying fundamental solitons and their stability. Unstable solitons transform into stable fundamental ones in both 1D and 2D lattice models.

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Area of Science:

  • Nonlinear dynamics
  • Lattice models
  • Soliton theory

Background:

  • Dynamical lattices with on-site second-harmonic-generating nonlinearity and harmonic intersite couplings are crucial for studying wave propagation.
  • Understanding solitary-wave solutions and their stability is essential in various physical systems.

Purpose of the Study:

  • To investigate various solitary-wave solutions in 1D and 2D dynamical lattices.
  • To examine the stability of fundamental and twisted-mode solitons.
  • To compare lattice results with continuum counterparts.

Main Methods:

  • Numerical analysis of solitary-wave solutions in 1D and 2D lattices.
  • Stability analysis of identified solitons.
  • Comparison of lattice soliton behavior with continuum models.

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Main Results:

  • Fundamental (single-hump) solitons were identified in both 1D and 2D lattices.
  • Stability limits for twisted-mode solitons in 1D and their 2D counterparts (including discrete vortices) were determined.
  • Unstable twisted-mode solitons were observed to transform into stable fundamental solitons.

Conclusions:

  • The study successfully identified and analyzed solitary-wave solutions in complex lattice models.
  • Stability of solitons is dependent on coupling constants and phase-mismatch parameters.
  • Lattice solitons exhibit unique stability properties and transformation dynamics compared to continuum models.