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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Feng, Jonathan

Managing Editor: Lesna-Szreter, Paulina

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IMPACT FACTOR 2016 (Open Physics): 0.745
IMPACT FACTOR 2016 (Central European Journal of Physics): 0.765

CiteScore 2016: 0.82

SCImago Journal Rank (SJR) 2015: 0.458
Source Normalized Impact per Paper (SNIP) 2015: 1.142

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ISSN
2391-5471
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Volume 12, Issue 12 (Dec 2014)

Issues

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

Abstract

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

  • [1] Z. Chen, M. Segev, D. N. Christodoulides, Rep. Prog. Phys. 75, 086401 (2012) http://dx.doi.org/10.1088/0034-4885/75/8/086401CrossrefGoogle Scholar

  • [2] Y. S. Kivshar, G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic press, California, 2003) Google Scholar

  • [3] V. E. Zakharov, A. B. Shabat, J. Exp. Theor. Phys. 34, 62 (1972) Google Scholar

  • [4] Y. V. Kartashov, B. A. Malomed, L. Torner, Rev. Mod. Phys. 83, 247 (2011) http://dx.doi.org/10.1103/RevModPhys.83.247CrossrefGoogle Scholar

  • [5] J. Hukriede, D. Runde, D. Kip, J. Phys. D: Appl. Phys. 36, R1 (2003) http://dx.doi.org/10.1088/0022-3727/36/3/201CrossrefGoogle Scholar

  • [6] K. Peithmann, J. Hukriede, K. Buze, E. Krätzig, Phys. Rev. B 61, 4615 (2000) http://dx.doi.org/10.1103/PhysRevB.61.4615CrossrefGoogle Scholar

  • [7] O. V. Borovkova, Y. V. Kartashov, L. Torner, B. A. Malomed, Phys. Rev. E 84, 035602(R) (2011) http://dx.doi.org/10.1103/PhysRevE.84.035602CrossrefGoogle Scholar

  • [8] O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, L. Torner, Opt. Lett. 36, 3088 (2011) http://dx.doi.org/10.1364/OL.36.003088CrossrefGoogle Scholar

  • [9] W.-P. Zhong, M. Belić, G. Assanto, B. A. Malomed, T. Huang, Phys. Rev. A 84, 043801 (2011) http://dx.doi.org/10.1103/PhysRevA.84.043801CrossrefGoogle Scholar

  • [10] Q. Tian, L. Wu, Y. Zhang, J.-F. Zhang, Phys. Rev. E 85, 056603 (2012) http://dx.doi.org/10.1103/PhysRevE.85.056603CrossrefGoogle Scholar

  • [11] V. E. Lobanov, O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, L. Torner, Opt. Lett. 37, 1799 (2012) http://dx.doi.org/10.1364/OL.37.001799CrossrefGoogle Scholar

  • [12] Y. V. Kartashov, V. E. Lobanov, B. A. Malomed, L. Torner, Opt. Lett. 37, 5000 (2012) http://dx.doi.org/10.1364/OL.37.005000CrossrefGoogle Scholar

  • [13] Y. Wu, Q. Xie, H. Zhong, L. Wen, Wenhua Hai, Phys. Rev. A 87, 055801 (2013) http://dx.doi.org/10.1103/PhysRevA.87.055801CrossrefGoogle Scholar

  • [14] R. Driben, Y. V. Kartashov, B. A. Malomed, T. Meier, L. Torner, Phys. Rev. Lett. 112, 020404 (2014) http://dx.doi.org/10.1103/PhysRevLett.112.020404CrossrefGoogle Scholar

  • [15] Y. V. Kartashov, V. A. Vysloukh, L. Torner, B. A. Malomed, Opt. Lett. 36, 4587 (2011) http://dx.doi.org/10.1364/OL.36.004587CrossrefGoogle Scholar

  • [16] O. V. Borovkova, Y. V. Kartashov, V. A. Vysloukh, V. E. Lobanov, B. A. Malomed, L. Torner, Opt. Express 20, 2657 (2012) http://dx.doi.org/10.1364/OE.20.002657CrossrefGoogle Scholar

  • [17] J. Zeng, B. A. Malomed, Phys. Rev. E 86, 036607 (2012) http://dx.doi.org/10.1103/PhysRevE.86.036607CrossrefGoogle Scholar

  • [18] Y. He, B. A. Malomed, Phys. Rev. A 87, 053812 (2013) http://dx.doi.org/10.1103/PhysRevA.87.053812CrossrefGoogle Scholar

  • [19] W. B. Cardoso, J. Zeng, A. T. Avelar, D. Bazeia, B. A. Malomed, Phys. Rev. E 88, 025201 (2013) http://dx.doi.org/10.1103/PhysRevE.88.025201CrossrefGoogle Scholar

  • [20] O. V. Borovkova, V. E. Lobanov, B. A. Malomed, Phys. Rev. A 85, 023845 (2012) http://dx.doi.org/10.1103/PhysRevA.85.023845CrossrefGoogle Scholar

  • [21] G. Roati, M. Zaccanti, C. D’Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, G. Modugno, Phys. Rev. Lett. 99, 010403 (2007) http://dx.doi.org/10.1103/PhysRevLett.99.010403CrossrefGoogle Scholar

  • [22] S. E. Pollack, D. Dries, M. Junker, Y. P. Chen, T. A. Corcovilos, R. G. Hulet, Phys. Rev. Lett. 102, 090402 (2009) http://dx.doi.org/10.1103/PhysRevLett.102.090402CrossrefGoogle Scholar

  • [23] C. Eckart, Phys. Rev. 35, 1303 (1930) http://dx.doi.org/10.1103/PhysRev.35.1303CrossrefGoogle Scholar

  • [24] A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, A. A. Sukhorukov, Phys. Rev. Lett. 106, 193903 (2011). http://dx.doi.org/10.1103/PhysRevLett.106.193903CrossrefGoogle Scholar

  • [25] A. A. Sukhorukov, Opt. Lett. 35, 989 (2010) http://dx.doi.org/10.1364/OL.35.000989CrossrefGoogle Scholar

  • [26] J. Yang, J. Comp. Phys. 227, 6862 (2008) http://dx.doi.org/10.1016/j.jcp.2008.03.039CrossrefGoogle Scholar

  • [27] J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, Philadelphia, 2010) http://dx.doi.org/10.1137/1.9780898719680CrossrefGoogle Scholar

  • [28] C. H. Tstang, B. A. Malomed, K. W. Chow, Discrete Contin. Dyn. Syst. Ser. S 4, 1299 (2011) http://dx.doi.org/10.3934/dcdss.2011.4.1299CrossrefGoogle Scholar

About the article

Published Online: 2014-08-27

Published in Print: 2014-12-01


Citation Information: Open Physics, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-014-0517-0.

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