Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

• Authors: Qiongtao Xie
• Languages of publication: EN

Abstracts

EN

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

EN

exact solutions   bright and dark solitons   spatially inhomogeneous nonlinearity  

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 12
• Pages: 830-835

Dates

published

1 - 12 - 2014

online

27 - 8 - 2014

References

• [1] Z. Chen, M. Segev, D. N. Christodoulides, Rep. Prog. Phys. 75, 086401 (2012) http://dx.doi.org/10.1088/0034-4885/75/8/086401[Crossref]
• [2] Y. S. Kivshar, G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic press, California, 2003)
• [3] V. E. Zakharov, A. B. Shabat, J. Exp. Theor. Phys. 34, 62 (1972)
• [4] Y. V. Kartashov, B. A. Malomed, L. Torner, Rev. Mod. Phys. 83, 247 (2011) http://dx.doi.org/10.1103/RevModPhys.83.247[Crossref]
• [5] J. Hukriede, D. Runde, D. Kip, J. Phys. D: Appl. Phys. 36, R1 (2003) http://dx.doi.org/10.1088/0022-3727/36/3/201[Crossref]
• [6] K. Peithmann, J. Hukriede, K. Buze, E. Krätzig, Phys. Rev. B 61, 4615 (2000) http://dx.doi.org/10.1103/PhysRevB.61.4615[Crossref]
• [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.84.035602[Crossref]
• [8] O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, L. Torner, Opt. Lett. 36, 3088 (2011) http://dx.doi.org/10.1364/OL.36.003088[Crossref]
• [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.84.043801[Crossref]
• [10] Q. Tian, L. Wu, Y. Zhang, J.-F. Zhang, Phys. Rev. E 85, 056603 (2012) http://dx.doi.org/10.1103/PhysRevE.85.056603[Crossref]
• [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.37.001799[Crossref]
• [12] Y. V. Kartashov, V. E. Lobanov, B. A. Malomed, L. Torner, Opt. Lett. 37, 5000 (2012) http://dx.doi.org/10.1364/OL.37.005000[Crossref]
• [13] Y. Wu, Q. Xie, H. Zhong, L. Wen, Wenhua Hai, Phys. Rev. A 87, 055801 (2013) http://dx.doi.org/10.1103/PhysRevA.87.055801[Crossref]
• [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.112.020404[Crossref]
• [15] Y. V. Kartashov, V. A. Vysloukh, L. Torner, B. A. Malomed, Opt. Lett. 36, 4587 (2011) http://dx.doi.org/10.1364/OL.36.004587[Crossref]
• [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.20.002657[Crossref]
• [17] J. Zeng, B. A. Malomed, Phys. Rev. E 86, 036607 (2012) http://dx.doi.org/10.1103/PhysRevE.86.036607[Crossref]
• [18] Y. He, B. A. Malomed, Phys. Rev. A 87, 053812 (2013) http://dx.doi.org/10.1103/PhysRevA.87.053812[Crossref]
• [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.88.025201[Crossref]
• [20] O. V. Borovkova, V. E. Lobanov, B. A. Malomed, Phys. Rev. A 85, 023845 (2012) http://dx.doi.org/10.1103/PhysRevA.85.023845[Crossref]
• [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.99.010403[Crossref]
• [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.102.090402[Crossref]
• [23] C. Eckart, Phys. Rev. 35, 1303 (1930) http://dx.doi.org/10.1103/PhysRev.35.1303[Crossref]
• [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.106.193903[Crossref]
• [25] A. A. Sukhorukov, Opt. Lett. 35, 989 (2010) http://dx.doi.org/10.1364/OL.35.000989[Crossref]
• [26] J. Yang, J. Comp. Phys. 227, 6862 (2008) http://dx.doi.org/10.1016/j.jcp.2008.03.039[Crossref]
• [27] J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, Philadelphia, 2010) http://dx.doi.org/10.1137/1.9780898719680[Crossref]
• [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.2011.4.1299[Crossref]

Identifiers

DOI

10.2478/s11534-014-0517-0