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Optical soliton solutions of Manakov model arising in the description of wave propagation through optical fibers

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Abstract

In the field of nonlinear optics, soliton structures have been extensively investigated in recent years. Optical solitons can be used in communication systems as optical information carriers. The advantage of a optical soliton is that it does not alter its structure when it interacts with other pulses. Optical solitons are useful for signal processing applications like pulse compression, regeneration, and amplification, leading to cleaner, more reliable signals. They can also be explored in optical computing, sensing, and laser technology. Studying optical solitons provides insights into nonlinearity and dispersion in wave propagation, contributing to physics and paving the way for future discoveries. The purpose of this article is to strive for the optical soliton solutions of the Manakov model with the help of the modified auxiliary equation method and the extended trial equation method. The Manakov model is a simple, analytical, and numerical model that provides basic insights into soliton formation and propagation. This model is suitable for studying soliton properties like stability, interactions, and collisions. The study provides hyperbolic, trigonometric, rational, and notably, Jacobi-elliptic function solutions, which have not been explored for the considered system. Additionally, dark soliton, bright soliton, bright singular soliton, bright singular two-solitons, multi solitons and periodic solitary wave solutions are exhibited by their graphical representations.

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References

  • Abbagari, S., Houwe, A., Akinyemi, L., Bouetou, T.B.: Solitonic rogue waves induced by the modulation instability in a split-ring-resonator-based left-handed coplanar waveguide. Chin. J. Phys. (2023). https://doi.org/10.1016/j.cjph.2023.12.024

    Article  Google Scholar 

  • Abbagari, S., Houwe, A., Akinyemi, L., Doka, S.Y.: Modulation instability and nonlinear coupled-mode excitations in single-wall carbon nanotube. Eur. Phys. J. Plus 138, 1–12 (2023)

    Google Scholar 

  • Abbagari, S., Houwe, A., Akinyemi, L., Senol, M., Bouetou, T.B.: W-chirped solitons and modulated waves patterns in parabolic law medium with anti-cubic nonlinearity. J. Nonlinear Opt. Phys. Mater. (2023). https://doi.org/10.1142/S021886352350087X

    Article  Google Scholar 

  • Ahmed, H.M., El-Sheikh, M.M.A., Arnous, A.H., Rabie, W.B.: Construction of the soliton solutions for the Manakov system by extended simplest equation method. Int. J. Appl. Comput. Math. 7, 1–19 (2021)

    MathSciNet  Google Scholar 

  • Akram, G., Gillani, S.R.: Sub pico-second soliton with Triki-Biswas equation by the extended \((G^{\prime }/ G^2)\)-expansion method and the modified auxiliary equation method. Optik Int. J. Light Electron Opt. 229, 166227 (2021)

    Google Scholar 

  • Akram, G., Sadaf, M., Dawood, M., Baleanu, D.: Optical solitons for Lakshmanan-Porsezian-Daniel equation with Kerr law non-linearity using improved tan\((\frac{\psi (\eta )}{2})\) -expansion technique. Results Phys. 29, 104758 (2021)

    Google Scholar 

  • Akram, G., Sadaf, M., Khan, M.A.U.: Abundant optical solitons for Lakshmanan-Porsezian-Daniel model by the modified auxiliary equation method. Optik Int. J. Light Electron Opt. 251, 168163 (2022)

    Google Scholar 

  • Akram, G., Sadaf, M., Zainab, I.: The dynamical study of Biswas-Arshed equation via modified auxiliary equation method. Optik Int. J. Light Electron Opt. 255, 168614 (2022)

    Google Scholar 

  • Alquran, M., Jaradat, I., Baleanu, D.: Shapes and dynamics of dual-mode Hirota-Satsuma coupled KdV equations: exact traveling wave solutions and analysis. Chin. J. Phys. 58, 49–56 (2019)

    MathSciNet  Google Scholar 

  • Badshah, F., Tariq, K.U., Inc, M., Kazmi, S.M.R.: Solitons, stability analysis and modulation instability for the third order generalized nonlinear Schrödinger model in ultraspeed fibers. Opt. Quant. Electron. 55, 1094 (2023)

    Google Scholar 

  • Baskonus, H.M., Gao, W., Rezazadeh, H., Mirhosseini-Alizamini, S.M., Baili, J., Ahmad, H., Gia, T.N.: New classifications of nonlinear Schrödinger model with group velocity dispersion via new extended method. Results Phys. 31, 104910 (2021)

    Google Scholar 

  • Biswas, A., Yildirim, Y., Yaşar, E., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical soliton perturbation with quadratic-cubic nonlinearity using a couple of strategic algorithms. Chin. J. Phys. 56, 1990–1998 (2018)

    MathSciNet  Google Scholar 

  • Busch, T., Anglin, J.R.: Dark-bright solitons in inhomogeneous Bose-Einstein condensates. Phys. Rev. Lett. 87, 010401 (2001)

    ADS  Google Scholar 

  • Chen, L., Zhang, J.: A finite-dimensional integrable system related to the complex 3\(\times\) 3 spectral problem and the coupled nonlinear Schrödinger equation. World J. Eng. Technol. 3, 322 (2015)

    Google Scholar 

  • Chou, D., Ur Rehman, H., Amer, A., Amer, A.: New solitary wave solutions of generalized fractional Tzitzéica-type evolution equations using sardar sub-equation method. Opt. Quant. Electron. 55, 1148 (2023)

    Google Scholar 

  • Dhar, A.K., Das, K.P.: Fourth-order nonlinear evolution equation for two Stokes wave trains in deep water. Phys. Fluids A 3, 3021–3026 (1991)

    ADS  Google Scholar 

  • Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Ullah, M.Z., Zhou, Q., Triki, H., Moshokoa, S.P., Biswas, A.: Optical solitons with anti-cubic nonlinearity by extended trial equation method. Optik Int. J. Light Electron Opt. 136, 368–373 (2017)

    Google Scholar 

  • Esen, H., Secer, A., Ozisik, M., Bayram, M.: Dark, bright and singular optical solutions of the Kaup-Newell model with two analytical integration schemes. Optik Int. J. Light Electron Opt. 261, 169110 (2022)

    Google Scholar 

  • González-Gaxiola, O., Biswas, A., Ekici, M., Alshomrani, A.S.: Optical solitons with Sasa-Satsuma equation by Laplace-Adomian decomposition algorithm. Optik Int. J. Light Electron Opt. 229, 166262 (2021)

    Google Scholar 

  • Guan, W.Y., Li, B.Q.: Asymmetrical and self-similar structures of optical breathers for the Manakov system in photorefractive crystals and randomly birefringent fibers. Optik Int. J. Light Electron Opt. 194, 162882 (2019)

    Google Scholar 

  • Hasegawa, A.: An historical review of application of optical solitons for high speed communications. Chaos Interdiscip. J. Nonlinear Sci. 10, 475–485 (2000)

    MathSciNet  Google Scholar 

  • Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett. 23, 142–144 (1973)

    ADS  Google Scholar 

  • Haus, H.A., Wong, W.S.: Solitons in optical communications. Rev. Mod. Phys. 68, 423–444 (1996)

    ADS  Google Scholar 

  • Houwe, A., Abbagari, S., Akinyemi, L., Saliou, Y., Justin, M., Doka, S.Y.: Modulation instability, bifurcation analysis and solitonic waves in nonlinear optical media with odd-order dispersion. Phys. Lett. A 488, 129134 (2023)

    MathSciNet  Google Scholar 

  • Houwe, A., Abbagari, S., Doka, S.Y., Inc, M., Bouetou, T.B.: Clout of fractional time order and magnetic coupling coefficients on the soliton and modulation instability gain in the Heisenberg ferromagnetic spin chain. Chaos Solitons Fractals 151, 111254 (2021)

    MathSciNet  Google Scholar 

  • Iqbal, I., Rehman, H.U., Mirzazadeh, M., Hashemi, M.S.: Retrieval of optical solitons for nonlinear models with Kudryashov’s quintuple power law and dual-form nonlocal nonlinearity. Opt. Quant. Electron. 55, 588 (2023)

    Google Scholar 

  • Kivshar, Y.S., Peyrard, M.: Modulational instabilities in discrete lattices. Phys. Rev. A 46, 3198 (1992)

    ADS  Google Scholar 

  • Li, Z., Lian, Z.: Optical solitons and single traveling wave solutions for the Triki-Biswas equation describing monomode optical fibers. Optik Int. J. Light Electron Opt. 258, 168835 (2022)

    Google Scholar 

  • Li, M., Zhang, Y., Ye, R., Lou, Y.: Exact solutions of the nonlocal Gerdjikov-Ivanov equation. Commun. Theor. Phys. 73, 105005 (2021)

    MathSciNet  ADS  Google Scholar 

  • Mahak, N., Akram, G.: The modified auxiliary equation method to investigate solutions of the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity. Optik Int. J. Light Electron Opt. 207, 164467 (2020)

    Google Scholar 

  • Manakov, S.V.: On the theory of two-dimensional stationary self-focusing of electromagnetic waves. Soviet J. Exp. Theor. Phys. 38, 248–253 (1974)

    ADS  Google Scholar 

  • Meng, G.Q., Guo, H.C.: Mixed solutions for an AB-system in geophysical fluids or nonlinear optics. Appl. Math. Lett. 124, 107632 (2022)

    MathSciNet  Google Scholar 

  • Mukam, S.P., Abbagari, S., Houwe, A., Kuetche, V.K., Inc, M., Doka, S.Y., Bouetou, T.B., Akinlar, M.A.: Generalized Darboux transformation and higher-order rogue wave solutions to the Manakov system. Int. J. Mod. Phys. B 35, 2150260 (2021)

    ADS  Google Scholar 

  • Nguetcho, A.S.T., Wamba, É.: Effects of nonlinearity and substrate’s deformability on modulation instability in NKG equation. Commun. Nonlinear Sci. Numer. Simul. 50, 271–283 (2017)

    MathSciNet  ADS  Google Scholar 

  • Ozdemir, N., Esen, H., Secer, A., Bayram, M., Sulaiman, A., Yusuf, T., Aydin, A.H.: Optical solitons and other solutions to the Radhakrishnan-Kundu-Lakshmanan equation. Optik Int. J. Light Electron Opt. 242, 167363 (2021)

    Google Scholar 

  • Ozdemir, N., Esen, H., Secer, A., Bayram, M., Yusuf, A., Sulaiman, T.A.: Optical soliton solutions to Chen-Lee-Liu model by the modified extended tanh expansion scheme. Optik Int. J. Light Electron Opt. 245, 167643 (2021)

    Google Scholar 

  • Ozdemir, N., Secer, A., Ozisik, M., Bayram, M.: Perturbation of dispersive optical solitons with Schrödinger-Hirota equation with Kerr law and spatio-temporal dispersion. Optik Int. J. Light Electron Opt. 265, 169545 (2022)

    Google Scholar 

  • Pandir, Y., Gurefe, Y., Misirli, E.: The extended trial equation method for some time fractional differential equations. Discret. Dyn. Nat. Soc. (2013). https://doi.org/10.1155/2013/491359

    Article  MathSciNet  Google Scholar 

  • Radhakrishnan, R., Aravinthan, K.: A dark-bright optical soliton solution to the coupled nonlinear Schrödinger equation. J. Phys. A: Math. Theor. 40, 13023 (2007)

    ADS  Google Scholar 

  • Rehman, H.U., Awan, A.U., Allahyani, S.A., Tag-ElDin, E.M., Binyamin, M.A., Yasin, S.: Exact solution of paraxial wave dynamical model with Kerr media by using \(\phi ^6\) model expansion technique. Results Phys. 42, 105975 (2022)

    Google Scholar 

  • Rehman, H.U., Iqbal, I., Zulfiqar, H., Gholami, D., Rezazadeh, H.: Stochastic soliton solutions of conformable nonlinear stochastic systems processed with multiplicative noise. Phys. Lett. A 486, 129100 (2023)

    MathSciNet  Google Scholar 

  • Scott, A.C.: Launching a Davydov soliton: I. Soliton analysis. Phys. Scr. 29, 279 (1984)

    ADS  Google Scholar 

  • Shabat, A., Zakharov, V.: Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Soviet J. Exp. Theor. Phys. 34, 62–69 (1972)

    MathSciNet  ADS  Google Scholar 

  • Shi, D., Rehman, H.U., Iqbal, I., Miguel, V.C., Saleem, M.S., Zhang, X.: Analytical study of the dynamics in the double-chain model of DNA. Results Phys. 52, 106787 (2023)

    Google Scholar 

  • Tabi, C.B., Tagwo, H., Kofané, T.C.: Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity. Phys. Rev. E 106, 054201 (2022)

    MathSciNet  ADS  Google Scholar 

  • Tariq, K.U., Inc, M., Kazmi, S.M.R., Alhefthi, R.K.: Modulation instability, stability analysis and soliton solutions to the resonance nonlinear Schrödinger model with Kerr law nonlinearity. Opt. Quant. Electron. 55, 838 (2023)

    Google Scholar 

  • Triki, H., Sun, Y., Zhou, Q., Biswas, A., Yildirim, Y., Alshehri, H.M.: Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects. Chaos Solitons Fractals 164, 112622 (2022)

    MathSciNet  Google Scholar 

  • Triki, H., Zhou, Q., Liu, W., Biswas, A., Moraru, L., Yildirim, Y., Alshehri, H.M., Belic, M.R.: Chirped optical soliton propagation in birefringent fibers modeled by coupled Fokas-Lenells system. Chaos Solitons Fractals 155, 111751 (2022)

    MathSciNet  Google Scholar 

  • Yan, Z.: Vector financial rogue waves. Phys. Lett. A 375, 4274–4279 (2011)

    ADS  Google Scholar 

  • Yildirim, Y.: Optical solitons of Biswas-Arshed equation by modified simple equation technique. Optik Int. J. Light Electron Opt. 182, 986–994 (2019)

    Google Scholar 

  • Yildirim, Y., et al.: Bright, dark and singular optical solitons to Kundu-Eckhaus equation having four-wave mixing in the context of birefringent fibers by using of trial equation methodology. Optik Int. J. Light Electron Opt. 182, 110–118 (2019)

    Google Scholar 

  • Yildirim, Y.: Optical soliton molecules of Manakov model by modified simple equation technique. Optik Int. J. Light Electron Opt. 185, 1182–1188 (2019)

    Google Scholar 

  • Yildirim, Y.: Optical soliton molecules of Manakov model by trial equation technique. Optik Int. J. Light Electron Opt. 185, 1146–1151 (2019)

    Google Scholar 

  • Yildirim, Y.: Optical solitons with Biswas-Arshed equation by F-expansion method. Optik Int. J. Light Electron Opt. 227, 165788 (2021)

    Google Scholar 

  • Yildirim, Y., Yaşar, E.: Multiple exp-function method for soliton solutions of nonlinear evolution equations. Chin. Phys. B 26, 070201 (2017)

    ADS  Google Scholar 

  • Zayed, E.M.E., Shohib, R.M.A., Alngar, M.E.M., Nofal, T.A., Gepreel, K.A., Yildirim, Y.: Cubic-quartic optical solitons in magneto-optic waveguides for Biswas-Milovic equation with Kudryashov’s law of arbitrary refractive index. Optik Int. J. Light Electron Opt. 259, 168911 (2022)

    Google Scholar 

  • Zhu, W.H., Pashrashid, A., Adel, W., Gunerhan, H., Nisar, K.S., Saleel, C.A., Inc, M., Rezazadeh, H.: Dynamical behaviour of the foam drainage equation. Results Phys. 30, 104844 (2021)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Lahore, 54590, Pakistan

    Ghazala Akram, Maasoomah Sadaf, Saima Arshed & Mavra Farrukh

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  1. Ghazala Akram
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  2. Maasoomah Sadaf
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  3. Saima Arshed
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  4. Mavra Farrukh
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Contributions

Maasoomah Sadaf: Forrmal analysis, investigation, Data curation, Software, validation, review and editing of the manuscript. Saima Arshed: Conceptualization, Software, methodology, review and editing of the manuscript. Ghazala Akram: Conceptualization, Administration, validation, Supervision, Software, Visualization and writing of the manuscript. Mavra Farrukh: Formal analysis, methodology, validation, software and writing of the original draft. All authors read and approved the final manuscript.

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Correspondence to Ghazala Akram.

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Akram, G., Sadaf, M., Arshed, S. et al. Optical soliton solutions of Manakov model arising in the description of wave propagation through optical fibers. Opt Quant Electron 56, 906 (2024). https://doi.org/10.1007/s11082-024-06735-7

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