Abstract
Breathers and rogue waves are two special types of soliton and play significant role in optical fibers. In this work, the mixed breather and rogue wave solution is constructed for a variable coefficient inhomogeneous fiber system via the Darboux transformation method. The impacts on the mixed wave of the first- and second-order group velocity dispersions (GVD), are discussed, respectively. The spectral eigenvalue parameter control is also studied. The pulse wave width, amplitude and wave density can be controlled by the variable GVD functions and spectral eigenvalue parameter. Especially, two types of rogue wave solutions can be derived from the mixed solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agrawal, G.P.: Nonlinear Fiber Optics. Academic Press, San Diego (2001)
Agrawal, G.P.: Nonlinear Fiber Optics, 4th edn. Academic Press, San Diego (2007)
Akhmediev, N., Ankiewicz, A., Taki, M.: Waves that appear from nowhere and disappear without a trace. Phys. Lett. A 373, 675–678 (2009a)
Akhmediev, N., Soto-Crespo, J.M., Ankiewicz, A.: How to excite a rogue wave. Phys. Rev. A 80, 043818 (2009b)
Akhmediev, N., Dudley, J.M., Solli, D.R., Turitsyn, S.K.: Recent progress in investigating optical rogue waves. J. Opt. 15, 060201 (2013)
Arecchi, F.T., Bortolozzo, U., Montina, A., Residori, S.: Granularity and inhomogeneity are the joint generators of optical rogue waves. Phys. Rev. Lett. 106, 153901 (2011)
Becker, C., Stellmer, S., Soltan-Panahi, P., Dorscher, S., Baumert, M., Richter, E.M., Kronjager, J., Bongs, K., Sengstock, K.: Oscillations and interactions of dark and dark-bright solitons in Bose–Einstein condensates. Nat. Phys. 4, 496–501 (2008)
Du, Z., Tian, B., Chai, H.P., Sun, Y.: Darboux transformations, solitons, breathers and rogue waves for the modified Hirota equation with variable coefficients in an inhomogeneous fiber. Opt. Quantum Electron. 50, 83 (2018)
Dudley, J.M., Genty, G., Dias, F.: Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation. Opt. Express 17, 21497–21508 (2009)
Frisquet, B., Kibler, B., Millot, G.: Collision of Akhmediev breathers in nonlinear fiber optics. Phys. Rev. X 3, 041032 (2013)
Guo, B.L., Ling, L.M.: Rogue wave, breathers and bright-dark-rogue solutions for the coupled Schrödinger equations. Chin. Phys. Lett. 28, 110202 (2011)
Guo, R., Hao, H.Q.: Breathers and localized solitons for the Hirota–Maxwell–Bloch system on constant backgrounds in erbium doped fibers. Ann. Phys. 344, 10–16 (2014)
Guo, B.L., Ling, L.M., Liu, Q.P.: Nonlinear Schrödinger equation generalized Darboux transformation and rogue wave solutions. Phys. Rev. E 85, 026607 (2012)
He, J.S., Xu, S.W., Porsezian, K.: Rogue wave triggered at a critical frequency of a nonlinear resonant medium. Phys. Rev. E 93, 062201 (2016)
Husakou, A.V., Herrmann, J.: Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers. Phys. Rev. Lett. 87, 203901 (2001)
Khaykovich, L., Schreck, F., Ferrari, G., Bourdel, T., Cubizolles, J., Carr, L.D., Castin, Y., Salomon, C.: Formation of a matter-wave bright soliton. Science 296, 1290–1293 (2002)
Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N., Dudley, J.M.: The Peregrine soliton in nonlinear fibre optics. Nat. Phys. 6, 790–795 (2010)
Kolpakov, S.A., Kbashi, H., Sergeyev, S.V.: Dynamics of vector rogue waves in a fiber laser with a ring cavity. Optica 3, 870–875 (2016)
Kominis, Y.: Soliton dynamics in symmetric and non-symmetric complex potentials. Opt. Commun. 334, 265–272 (2015)
Li, B.Q., Ma, Y.L.: Solitons resonant behavior for a waveguide directional coupler system in optical fibers. Opt. Quantum Electron. 50, 270 (2018a)
Li, B.Q., Ma, Y.L.: Rogue waves for the optical fiber system with variable coefficients. Optik 158, 177–184 (2018b)
Li, B.Q., Ma, Y.L.: Lax pair, Darboux transformation and Nth-order rogue wave solutions for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation. Comput. Math. Appl. 77, 514–524 (2019a)
Li, B.Q., Ma, Y.L.: Periodic and \(N\)-kink-like optical solitons for a generalized Schrödinger equation with variable coefficients in an inhomogeneous fiber system. Optik 179, 854–860 (2019b)
Li, B.Q., Ma, Y.L., Yang, T.M.: The oscillating collisions between the three solitons for a dual-mode fiber coupler system. Superlattices Microstruct. 110, 126–132 (2017)
Lin, X.G., Liu, W.J., Lei, M.: Oscillationg solitons in nonlinear optics. Pramana J. Phys. 86, 575–580 (2016)
Liu, M., Luo, A.P., Luo, Z.C., Xu, W.C.: Dynamic trapping of a polarization rotation vector soliton in a fiber laser. Opt. Lett. 42, 330–333 (2017)
Liu, M., Li, H., Luo, A.P., Cui, H., Xu, W.C., Luo, Z.C.: Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser. J. Opt. 20, 034010 (2018)
Ma, Y.L.: Interaction and energy transition between the breather and rogue wave for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in optical fibers. Nonlinear Dyn. 97, 95–105 (2019)
Ma, Y.L., Li, B.Q.: Doubly periodic waves, bright and dark solitons for a coupled monomode step-index optical fiber system. Opt. Quantum Electron. 50, 443 (2018)
Messouber, A., Triki, H., Azzouzi, F., Zhou, Q., Biswas, A., Moshokoa, S.P., Belic, M.: Propagation properties of dipole-managed solitons through an inhomogeneous cubic-quintic-septic medium. Opt. Commun. 425, 64–70 (2018)
Musslimani, Z.H., Makris, K.G., El-Ganainy, R., Christodoulides, D.N.: Optical solitons in PT periodic potentials. Phys. Rev. Lett. 100, 030402 (2008)
Park, I.Y., Kim, S., Choi, J., Lee, D.H., Kim, Y.J., Kling, M.F., Stockman, M.I., Kim, S.W.: Plasmonic generation of ultrashort extreme-ultraviolet light pulses. Nat. Photonics 5, 678–682 (2011)
Sekikawa, T., Kosuge, A., Kanai, T., Watanabe, S.: Nonlinear optics in the extreme ultraviolet. Nature 432, 605–608 (2004)
Solli, D.R., Ropers, C., Koonath, P., Jalali, B.: Optical rogue waves. Nature 450, 1054 (2007)
Suret, P., El Koussaifi, R., Tikan, A.: Single-shot observation of optical rogue waves in integrable turbulence using time microscopy. Nat. Commun. 7, 13136 (2016)
Wang, Y., Li, L.: Optical amplification and reshaping based on rogue wave in the femtosecond regime. Rom. J. Phys. 62, 205 (2017)
Wang, L., Li, X., Qi, F.H., Zhang, L.L.: Breather interactions and higher-order nonautonomous rogue waves for the inhomogeneous nonlinear Schrödinger Maxwell–Bloch equations. Ann. Phys. 359, 97–114 (2015)
Wang, Y., Song, L.J., Li, L.: Optical amplification and reshaping based on the Peregrine rogue wave. Appl. Opt. 55, 7241–7246 (2016)
Wen, X.Y., Yan, Z.Y.: Higher-order rational solitons and rogue-like wave solutions of the (2+1)-dimensional nonlinear fluid mechanics equations. Commun. Nonlinear Sci. 43, 311–329 (2017)
Xie, X.Y., Tian, B., Wang, Y.F.: Rogue wave solutions for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber. Ann. Phys. 362, 884 (2015)
Yan, Z.Y.: Two-dimensional vector rogue wave excitations and controlling parameters in the two-component Gross–Pitaevskii equations with varying potentials. Nonlinear Dyn. 79, 2515–2529 (2015)
Yu, X.L., Cao, C.B., Zhu, H.S., Li, Q.S., Liu, C.L., Gong, Q.H.: Nanometer-sized copper sulfide hollow spheres with strong optical-limiting properties. Adv. Funct. Mater. 17, 1397–1401 (2007)
Yu, W.T., Zhou, Q., Mirzazadeh, M., Liu, W.J., Biswas, A.: Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics. J. Adv. Res. 15, 69–76 (2019)
Acknowledgements
This work was supported partially by the National Natural Science Foundation of China Grant No. (61702020), Beijing Natural Science Foundation Grant No. (4172013) and Beijing Natural Science Foundation-Haidian Primitive Innovation Joint Fund Grant No. (L182007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Guan, WY., Li, BQ. Mixed structures of optical breather and rogue wave for a variable coefficient inhomogeneous fiber system. Opt Quant Electron 51, 352 (2019). https://doi.org/10.1007/s11082-019-2060-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-019-2060-0