Abstract
We study multi-peak solitons on a plane-wave background in an erbium-doped fiber system with some higher-order effects, which is governed by a coupled Hirota and Maxwel-Bloch (H-MB) model. The important characteristics of multi-peak solitons induced by the higher-order effects, such as the velocity changes, localization or periodicity attenuation, and state transitions, are revealed in detail. In particular, our results demonstrate explicitly that a multi-peak soliton can be converted to an anti-dark soliton when the periodicity vanishes; on the other hand, a multi-peak soliton is transformed to a periodic wave when the localization vanishes. Numerical simulations are performed to confirm the propagation stability of multi-peak solitons riding on a plane-wave background. Finally, we compare and discuss the similarity and difference of multi-peak solitons in special degenerate cases of the H-MB system with general existence conditions.
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References
A.I. Maimistov, A.M. Basharov, Nonlinear Optical Waves (Springer-Verlag, Berlin, 1999)
S. Kakei, J. Satsuma, J. Phys. Soc. Jpn 63, 885 (1994)
K. Porsezian, K. Nakkeeran, J. Mod. Opt. 42, 1953 (1995)
K. Porsezian, J. Mod. Opt. 47, 1635 (2000)
K. Porsezian, P. Seenuvasakumaran, R. Ganapathy, Phys. Lett. A 348, 233 (2006)
M.S.M. Rajan, A. Mahalingam, A. Uthayakumar, J. Opt. 14, 105204 (2012)
K. Porsezian, K. Nakkeeran, Phys. Rev. Lett. 74, 2941 (1995)
K. Nakkeeran, K. Porsezian, J. Phys. A 28, 3817 (1995)
K. Nakkeeran, K. Porsezian, Opt. Commun. 123, 169 (1996)
M. Nakazawa, E. Yamada, H. Kubota, Phys. Rev. Lett. 66, 2625 (1991)
M. Nakazawa, E. Yamada, H. Kubota, Phys. Rev. A 44, 5973 (1991)
M. Nakazawa, Y. Kimura, K. Kurokawa, K. Suzuki, Phys. Rev. A 45, R23 (1992)
M. Nakazawa, K. Suzuki, Y. Kimura, H. Kubota, Phys. Rev. A 45, R2682 (1992)
N. Akhmediev, J.M. Soto-Crespo, A. Ankiewicz, Phys. Lett. A 373, 2137 (2009)
N. Akhmediev, A. Ankiewicz, M. Taki, Phys. Lett. A 373, 675 (2009)
N. Akhmediev, J.M. Soto-Crespo, A. Ankiewicz, Phys. Rev. A 80, 043818 (2009)
J.M. Dudley, F. Dias, M. Erkintalo, G. Genty, Nat. Photon. 8, 755 (2014)
N. Akhmediev, J.M. Dudley, D.R. Solli, S.K. Turitsyn, J. Opt. 15, 060201 (2013)
N. Akhmediev et al., J. Opt. 18, 063001 (2016)
J.S. He, S.W. Xu, K. Porsezian, J. Phys. Soc. Jpn 81, 033002 (2012)
J.S. He, S.W. Xu, K. Porsezian, Phys. Rev. E 86, 066603 (2012)
C.Z. Li, J.S. He, K. Porsezian, Phys. Rev. E 87, 012913 (2013)
R. Guo, H.Q. Hao, Commun. Nonlinear Sci. Numer. Simulat. 19, 3529 (2014)
R. Guo, H.Q. Hao, Ann. Phys. 344, 10 (2014)
L. Wang, X. Li, F.H. Qi, L.L. Zhang, Ann. Phys. 359, 97 (2015)
Y. Ren, Z.Y. Yang, C. Liu, W.L. Yang, Phys. Lett. A 379, 2991 (2015)
L. Wang, Y.J. Zhu, J.H. Zhang, T. Xu, F.H. Qi, Y.S. Xue, J. Phys. Soc. Jpn 85, 024001 (2016)
G.P. Agrawal, J. Opt. Soc. Am. B 28, A1 (2011)
G.P. Agrawal, Nonlinear Fiber Optics, 4th edn. (Academic Press, Boston, 2007)
N. Akhmediev, A. Ankiewicz, Solitons: Non-linear Pulses and Beams (Chapman and Hall, London, 1997)
J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, Philadelphia, 2010)
A. Ankiewicz, N. Akhmediev, Phys. Lett. A 378, 358 (2014)
A. Chowdury, D.J. Kedziora, A. Ankiewicz, N. Akhmediev, Phys. Rev. E 90, 032922 (2014)
R. Guo, B. Tian, X. Lü, H.Q. Zhang, W.J. Liu Comput. Math. Phys. 52, 565 (2012)
R. Guo, H.Q. Hao, L.L. Zhang, Mod. Phys. Lett. B 27, 1350130 (2013)
A. Chowdury, D.J. Kedziora, A. Ankiewicz, N. Akhmediev, Phys. Rev. E 91, 032928 (2015)
A. Chowdury, A. Ankiewicz, N. Akhmediev, Proc. R. Soc. A 471, 20150130 (2015)
L. Wang, J.H. Zhang, Z.Q. Wang, C. Liu, M. Li, F.H. Qi, R. Guo, Phys. Rev. E 93, 012214 (2016)
L. Wang, J.H. Zhang, C. Liu, M. Li, F.H. Qi, arXiv:1603.01456
C. Liu, Z.Y. Yang, L.C. Zhao, L. Duan, G.Y. Yang, W.L. Yang, arXiv:1603.04554
A. Ankiewicz, J.M. Soto-Crespo, N. Akhmediev, Phys. Rev. E 81, 046602 (2010)
A. Ankiewicz, J.M. Soto-Crespo, M.A. Chowdhury, N. Akhmediev, J. Opt. Soc. Am. B 30, 87 (2013)
G.Y. Yang, L. Li, S.T. Jia, Phys. Rev. E 85, 046608 (2012)
Y.S. Tao, J.S. He, Phys. Rev. E 85, 026601 (2012)
C. Liu, Z.Y. Yang, L.C. Zhao, W.L. Yang, Phys. Rev. E 91, 022904 (2015)
A. Ankiewicz, Y. Wang, S. Wabnitz, N. Akhmediev, Phys. Rev. E 89, 012907 (2014)
A. Chowdury, D.J. Kedziora, A. Ankiewicz, N. Akhmediev, Phys. Rev. E 91, 022919 (2015)
L.C. Zhao, C. Liu, Z.Y. Yang, Commun. Nonlinear Sci. Numer. Simulat. 20, 9 (2015)
Yu.S. Kivshar, Phys. Rev. A 43, 1677 (1991)
Yu.S. Kivshar, V.V. Afanasjev, Phys. Rev. A 44, 1446(R) (1991)
R. Hirota, J. Math. Phys. 14, 805 (1973)
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Ren, Y., Yang, ZY., Liu, C. et al. Characteristics of optical multi-peak solitons induced by higher-order effects in an erbium-doped fiber system. Eur. Phys. J. D 70, 187 (2016). https://doi.org/10.1140/epjd/e2016-70079-7
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DOI: https://doi.org/10.1140/epjd/e2016-70079-7