## Properties of soliton solutions on a cw background in optical fibers with higher-order effects

JOSA B, Vol. 21, Issue 12, pp. 2089-2094 (2004)

http://dx.doi.org/10.1364/JOSAB.21.002089

Enhanced HTML Acrobat PDF (210 KB)

### Abstract

The *N*-soliton solutions for the integrable Hirota equation describing pulse propagation in optical fibers with higher-order effects are presented by using the Darboux transformation method. As an example, the general one-soliton solution on a cw background is given in its explicit form. Then, two exact analytic solutions that describe (i) modulation instability and (ii) bright pulse propagation on a cw background are discussed in detail. The simulations performed in selected cases show that these soliton solutions can be generated numerically when the involved parameters do not exactly satisfy the required integrability conditions.

© 2004 Optical Society of America

**OCIS Codes**

(060.4080) Fiber optics and optical communications : Modulation

(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons

(190.4370) Nonlinear optics : Nonlinear optics, fibers

**Citation**

Shuqing Li, Lu Li, Zhonghao Li, and Guosheng Zhou, "Properties of soliton solutions on a cw background in optical fibers with higher-order effects," J. Opt. Soc. Am. B **21**, 2089-2094 (2004)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-21-12-2089

Sort: Year | Journal | Reset

### References

- A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersion dielectric fibers. 1. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973). [CrossRef]
- A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, UK, 1995).
- G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1995).
- Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987). [CrossRef]
- R. Hirota, “Exact envelope-soliton solution of a nonlinear wave equation,” J. Math. Phys. 14, 805–809 (1973). [CrossRef]
- N. Sasa and J. Satsuma, “New-type soliton solution for a higher-order nonlinear Schrödinger equation,” J. Phys. Soc. Jpn. 60, 409–417 (1991). [CrossRef]
- D. Mihalache, L. Torner, F. Moldoveanu, N.-C. Panoiu, and N. Truta, “Inverse scattering approach to femtosecond solitons in monomode optical fibers,” Phys. Rev. E 48, 4699–4709 (1993). [CrossRef]
- D. Mihalache, N.-C. Panoiu, F. Moldoveanu, and D.-M. Baboiu, “The Riemann problem method for solving a perturbed nonlinear Schrödinger equation describing pulse propagation in optic fibers,” J. Phys. A: Math. Gen. 27, 6177–6189 (1994). [CrossRef]
- K. Porsezian and K. Nakkeeran, “Optical solitons in presence of Kerr dispersion and self-frequency shift,” Phys. Rev. Lett. 76, 3955–3958 (1996). [CrossRef] [PubMed]
- M. Gedalin, T. C. Scott, and Y. B. Band, “Optical solitary waves in the higher-order nonlinear Schrödinger equation,” Phys. Rev. Lett. 78, 448–451 (1997). [CrossRef]
- D. Mihalache, N. Truta, and L. C. Crasovan, “Painleve analysis and bright solitary waves of the higher-order nonlinear Schrödinger equation containing third-order dispersion and self-steepening term,” Phys. Rev. E 56, 1064–1070 (1997). [CrossRef]
- Z. H. Li, G. S. Zhou, and D. C. Su, “N-soliton solution in the higher order nonlinear Schrödinger equation,” in Fiber Optic Components and Optical Communication II, S. Jian, F. F. Tong, and R. Maerz, eds., Proc. SPIE 3552, 226–231 (1998). [CrossRef]
- Y. S. Kivshar and V. V. Afanasjev, “Dark optical solitons with reverse-sign amplitude,” Phys. Rev. A 44, R1446–R1449 (1991). [CrossRef] [PubMed]
- R. Radhakrishnam and M. Lakshmanan, “Exact soliton solutions to coupled nonlinear Schrödinger equations with higher-order effects,” Phys. Rev. E 54, 2949–2955 (1996). [CrossRef]
- S. L. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, “Dark solitary waves in the nonlinear Schrödinger equation with third-order dispersion, self-steepening, and self-frequency shift,” Phys. Rev. E 60, R45–R47 (1999). [CrossRef]
- A. Mahalingam and K. Porsezian, “Propagation of dark solitons with higher-order effects in optical fibers,” Phys. Rev. E 64, 046608 (2001). [CrossRef]
- L. Li, Z. H. Li, Z. Y. Xu, G. S. Zhou, and K. H. Spatscheck, “Gray optical dips in subpicosecond regime,” Phys. Rev. E 66, 046616 (2002). [CrossRef]
- Z. H. Li, L. Li, H. P. Tian, and G. S. Zhou, “New types of solitary wave solution for the higher nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000). [CrossRef] [PubMed]
- W. P. Hong, “Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic non-Kerr terms,” Opt. Commun. 194, 217–223 (2001). [CrossRef]
- N. N. Akhmediev and N. V. Mitzkevich, “Extremely high degree of N-soliton pulse compression in an optical fiber,” IEEE J. Quantum Electron. 27, 849–857 (1991). [CrossRef]
- Z. Y. Xu, L. Li, Z. H. Li, and G. S. Zhou, “Modulation instability and solitons on a cw background in an optical fiber with higher-order effects,” Phys. Rev. E 67, 026603 (2003). [CrossRef]
- L. Li, Z. H. Li, S. Q. Li, and G. S. Zhou, “Modulation instability and solitons on a cw background in inhomogeneous optical fiber media,” Opt. Commun. 234, 169–176 (2004). [CrossRef]
- V. B. Matveev and M. A. Salli, Darboux Transformations and Solitons, Springer Series in Nonlinear Dynamics (Springer-Verlag, Berlin, 1991).
- Q. H. Park and H. J. Shin, “Parametric control of soliton light traffic by cw traffic light,” Phys. Rev. Lett. 82, 4432–4435 (1999). [CrossRef]
- M. J. Ablowitz and P. A. Clarkson, Soliton, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University, London, 1991).
- G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987). [CrossRef] [PubMed]
- D. Mihalache and N. C. Panoiu, “Analytic method for solving the nonlinear Schrödinger equation describing pulse propagation in dispersive optic fibres,” J. Phys. A: Math. Gen. 26, 2679–2697 (1993). [CrossRef]
- D. Mihalache, F. Lederer, and D.-M. Baboiu, “Two-parameter family of exact solutions of the nonlinear Schrödinger equation describing optical soliton propagation,” Phys. Rev. A 47, 3285–3290 (1993). [CrossRef] [PubMed]
- L. Gagnon, “Solitons on a continuous-wave background and collision between two dark pulses: some analytical results,” J. Opt. Soc. Am. B 10, 469–474 (1993). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.