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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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Volume 12, Issue 12


Volume 13 (2015)

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

Qiongtao Xie
  • School of Physics and Electronic Engineering, Hainan Normal University, Haikou, 571158, China
  • Department of Physics, Hunan Normal University, Changsha, 410081, China
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Published Online: 2014-08-27 | DOI: https://doi.org/10.2478/s11534-014-0517-0


We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing (SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable.

Keywords: exact solutions; bright and dark solitons; spatially inhomogeneous nonlinearity

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About the article

Published Online: 2014-08-27

Published in Print: 2014-12-01

Citation Information: Open Physics, Volume 12, Issue 12, Pages 830–835, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-014-0517-0.

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