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Two-dimensional dissipative gap solitons.

Hidetsugu Sakaguchi1, Boris A Malomed

  • 1Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 2, 2009
PubMed
Summary
This summary is machine-generated.

This study constructs stable 2D dissipative gap solitons (DGSs) using a complex Ginzburg-Landau model with loss, gain, and periodic potentials. Analytical and numerical methods confirm the existence of fundamental and vortical DGSs.

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Area of Science:

  • Nonlinear Optics
  • Mathematical Physics

Background:

  • Dissipative systems exhibit unique soliton dynamics.
  • Gap solitons form within the forbidden band gaps of a linear spectrum.
  • Complex Ginzburg-Landau equation models various physical phenomena.

Purpose of the Study:

  • To construct and analyze stable two-dimensional dissipative gap solitons (DGSs).
  • To investigate both fundamental and vortical DGSs within a specific nonlinear system.
  • To develop and validate analytical approximations for DGSs.

Main Methods:

  • Integration of the complex Ginzburg-Landau equation in 2D.
  • Inclusion of linear-cubic-quintic loss/gain, self-defocusing nonlinearity, and periodic potential.
  • Numerical simulations and analytical approximation (variational method and balance equation).

Main Results:

  • Stable 2D dissipative gap solitons (fundamental and vortical) were successfully constructed.
  • Soliton families were found to reside in the first finite band gap of the linear spectrum.
  • Analytical approximations showed good agreement with numerical findings.

Conclusions:

  • The developed model supports stable 2D dissipative gap solitons.
  • The findings offer a theoretical basis for implementing these solitons in optical systems.
  • The study validates a combined numerical and analytical approach for soliton analysis.