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Optical soliton with Kudryashov’s equation via sine-Gordon expansion and Kudryashov methods

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Abstract

This article is concerned with analyzing exact optical soliton solutions to Kudryashov’s model. To this end, the sine-Gordon expansion and Kudryashov methods are exerted and a bunch of new optical soliton solutions is acquired. The implementation and algebraic methods are discussed in detail. Finally, singular and bright-dark soliton solutions emerge from the scheme and the existing criteria for such solutions are elucidated.

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References

  • Akinyemi, L., Senol, M., Huseen, S.N.: Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma. Adv. Differ. Equ. 2021, 1–27 (2021)

  • Akinyemi, L., Senol, M., Iyiola, O.S.: Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method. Math. Comput. Simul. 182, 211–233 (2021)

  • Akinyemi, L., Senol, M., Mirzazadeh, M., Eslami, M.: Optical solitons for weakly nonlocal Schrödinger equation with parabolic law nonlinearity and external potential. Optik 230, 166281 (2021)

  • Ali, S., Younis, M.: Rogue wave solutions and modulation instability with variable coefficient and harmonic potential. Front. Phys. 7, 255 (2020)

    Article  Google Scholar 

  • Bai, C.: Exact solutions for nonlinear partial differential equation: a new approach. Phys. Lett. A 288, 191–195 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Biswas, A., Sonmezoglu, A., Ekici, M., Alshomrani, A.S., Belic, M.R.: Optical solitons with Kudryashov’s equation by F-expansion. Optik 199, 163338 (2019)

  • Biswas, A., Ekici, M., Sonmezoglu, A., Alshomrani, A.S., Belic, M.R.: Optical solitons with Kudryashov’s equation by extended trial function. Optik 202, 163290 (2020a)

  • Biswas, A., Vega-Guzman, J., Ekici, M., Zhou, Q., Triki, H., Alshomrani, A.S., Belic, M.R.: Optical solitons and conservation laws of Kudryashov’s equation using undetermined coefficients. Optik 202, 163417 (2020b)

  • Dai, C.Q., Fan, Y., Zhang, N.: Re-observation on localized waves constructed by variable separation solutions of (1+1)-dimensional coupled integrable dispersionless equations via the projective Riccati equation method. Appl. Math. Lett. 96, 20–26 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Emplit, P., Hamaide, J.P., Reynaud, F., Froehly, C., Barthelemy, A.: Picosecond steps and dark pulses through nonlinear single mode fibers. Opt. Commun. 62, 374–379 (1987)

    Article  ADS  Google Scholar 

  • Ghanbari, B., Nisar,K.S., Aldhaifallah, M.: Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method. Adv. Differ. Equ. 2020, 1–25 (2020)

  • Ghanbari, B., Yusuf, A., Baleanu, D.: The new exact solitary wave solutions and stability analysis for the (2+1)-dimensional Zakharov–Kuznetsov equation. Adv. Differ. Equ. 2019, 1–15 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Ghanbari, B., Inc, M., Rada, L.: Solitary wave solutions to the Tzitzeica type equations obtained by a new efficient approach. J. Appl. Anal. Comput. 9, 568–589 (2019)

    MathSciNet  MATH  Google Scholar 

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

  • Hashemi, M.S., Inc, M., Bayram, M.: Symmetry properties and exact solutions of the time fractional Kolmogorov–Petrovskii–Piskunov equation. Rev. Mex. Física 65(5), 529–535 (2019)

  • Hashemi, M.S., Akgül, A.: Solitary wave solutions of time–space nonlinear fractional Schrödinger’s equation: two analytical approaches. J. Comput. Appl. Math. 339, 147–160 (2018)

  • Hosseini, K., Ayati, Z., Ansari, R.: New exact solution of the Tzitzé ica type equations in nonlinear optics using the function method. J. Mod. Opt. 65, 847–851 (2017)

    Article  ADS  Google Scholar 

  • Hosseini, K., Zabihi, A., Samadani, F., Ansari, R.: New explicit exact solutions of the unstable nonlinear Schrödinger’s equation using the and hyperbolic function methods. Opt. Quant. Electron. 50, 82 (2018)

  • Hosseini, K., Ansari, R., Samadani, F., Zabihi, A., Shafarodi, A., Mirzazadeh, M.: High-order dispersive cubic–quintic Schrödinger equation and its soliton solutions. Acta Phys. Pol. A 136, 1 (2019)

    Article  Google Scholar 

  • Hubert, M.B., Betchewe, G., Doka, S.Y., Crepin, K.T.: Soliton wave solutions for the nonlinear transmission line using the Kudryashov method and the \(G^{\prime }/G\)-expansion method. Appl. Math. Comput. 234, 229–309 (2019)

    MATH  Google Scholar 

  • Hussain, A., Jhangeer, A., Abbas, N., Khan, I., Sherif, E.S.M.: Optical solitons of fractional complex Ginzburg–Landau equation with conformable, beta, and M-truncated derivatives: a comparative study. Adv. Differ. Equ. 2020, 1–19 (2020)

    Article  MathSciNet  Google Scholar 

  • Inc, M., Kilic, B.: The first integral method for the perturbed Wadati–Segur–Ablowitz equation with time dependent coefficient. Kuwait J. Sci. 43, 81–88 (2016)

    MathSciNet  MATH  Google Scholar 

  • Inc, M., Ates, E., Tchier, F.: Optical solitons of the coupled nonlinear Schrdingers equation with spatiotemporal dispersion. Nonlinear Dyn. 85, 1319–1329 (2016)

    Article  MATH  Google Scholar 

  • Inc, M., Kilic, B., Baleanu, D.: Optical soliton solutions of the pulse propagation generalized equation in parabolic-law media with space-modulated coeefficients. Optik 127, 1056–1058 (2016)

    Article  ADS  Google Scholar 

  • Jhangeer, A., Hussain, A., Junaid-U-Rehman, M., Baleanu, D., Riaz, M.B.: Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation. Chaos Solitons Fract. 143, 110578 (2021)

  • Khater, M.M.A., Attia, R.A., Lu, D.: Explicit lump solitary wave of certain interesting (3+1)-dimensional waves in physics via some recent traveling wave methods. Entropy 21(4), 397 (2019a)

    Article  ADS  MathSciNet  Google Scholar 

  • Khater, M.M.A., Attia, R.A., Lu, D.: Modified auxiliary equation method versus three nonlinear fractional biological models in present explicit wave solutions. Math. Comput. Appl. 24(1), 1 (2019b)

    MathSciNet  Google Scholar 

  • Khater, M.M., Inc, M., Attia, R.A., Lu, D.: Abundant new computational wave solutions of the GM-DP-CH equation via two modified recent computational schemes. J. Taibah Univ. Sci. 14(1), 1554–1562 (2020)

    Article  Google Scholar 

  • Kilic, B., Inc, M.: On optical solitons of the resonant Schrodingers equation in optical fibers with dual-power law nonlinearity and time-dependent coeffcients. Waves Random Complex Media 25, 245–251 (2015)

    Article  MATH  Google Scholar 

  • Korkmaz, A., Hepson, O.E., Hosseini, K., Rezazadeh, H.: Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-Class. J. King Saud Univ. 32(1), 567–574 (2020)

    Article  Google Scholar 

  • Korpinar, Z., Inc, M., Bayram, M., Hashemi, M.S.: New optical solitons for Biswas–Arshed equation with higher order dispersions and full nonlinearity. Optik 206, 163332 (2020)

  • Krishnan, E.V., Kumar, S., Biswas, A.: Solitons and other nonlinear waves of the Boussinesq equation. Nonlinear Dyn. 70, 1213–1221 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Kudryashov, N.A.: A generalized model for description of propagation pulses in optical fiber. Int. J. Light Electron Opt. 189, 42–52 (2019)

    Article  Google Scholar 

  • Kumar, S., Malik, S., Belic, M.R.: Optical solitons with Kudryashov’s equation by Lie symmetry analysis. Phys. Wave Phen. 28, 299–304 (2020)

  • Kumar, S., Malik, S., Biswas, A.: A re-visitation to reported results on optical solitons. Chaos Soliton Fractals 137, 109855 (2020)

  • Kumar, D., Hosseini, K., Samadani, F.: The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzé ica type equations in nonlinear optics. Optik 149, 439–446 (2017)

    Article  ADS  Google Scholar 

  • Mallenauer, L.F., Stolen, R.H., Gordon, J.P.: Experimental investigation of picosecond pulse narrowing and solitons in optical fibers. Phys. Rev. Lett. 43, 13 (1980)

    Google Scholar 

  • Martinez, H.Y., Gomez-Aguilar, J.F., Baleanu, D.: Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion. Optik 155, 357–365 (2018)

    Article  ADS  Google Scholar 

  • Martinez, H.Y., Rezazadeh, H., Souleymanou, A., Mukam, S.P.T., Eslami, M., Kuetche, V.K., Bekir, A.: The extended modified method applied to optical solitons solutions in birefringent fibers with weak nonlocal nonlinearity and four wave mixing. Chin. J. Phys. 58, 137–150 (2019)

    Article  Google Scholar 

  • Munawar, M., Jhangeer, A., Pervaiz, A., Ibraheem, F.: New general extended direct algebraic approach for optical solitons of Biswas–Arshed equation through birefringent fibers. Optik 228, 165790 (2021)

  • Munusamy, K., Ravichandran, C., Nisar, K.S., Ghanbari, B.: Existence of solutions for some functional integrodifferential equations with nonlocal conditions. Math. Methods Appl. Sci. 43(17), 10319–10331 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Musammil,N.M., Porsezian,K., Nithyanandan, K., Subha,P.A., Tchofo Dinda, P.: Ultrashort dark solitons interactions and nonlinear tunneling in the modified nonlinear Schrödinger equation with variable coefficient. Opt. Fiber Technol. 37, 11–20 (2017)

  • Osman, M.S., Lu, D., Khater, M.M.A., Attia, R.A.: Complex wave structures for abundant solutions related to the complex Ginzburg–Landau model. Optik 192, 162927 (2019)

  • Park, C., Nuruddeen, R.I., Khalid, K.A., Lawal, M., Osman, M.S., Baleanu, D.: Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations. Adv. Differ. Equ. 2020, 627 (2020)

    Article  MathSciNet  Google Scholar 

  • Qian, L., Attia, R.A., Qiu, Y., Lu, D., Khater, M.M.A.: The shock peakon wave solutions of the general Degasperis–Procesi equation. Int. J. Modern Phys. B (2019). https://doi.org/10.1142/S0217979219503508

    Article  MathSciNet  Google Scholar 

  • Raslan, K.R., Khalid, K.A.: A new structure formulations for cubic B-spline collocation method in three and four-dimensions. Nonlinear Eng. 9, 432–448 (2020)

    Article  ADS  Google Scholar 

  • Raslan, K.R., El-Danaf, T.S., Ali, K.K.: Exact solution of space-time fractional coupled EW and coupled MEW equations using modified Kudryashov method. Commun. Theor. Phys. 68, 49–56 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Raza, N., Javid, A.: Generalization of optical solitons with dual dispersion in the presence of Kerr and quadratic–cubic law nonlinearities. Mod. Phys. Lett. B 33(01), 1850427 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  • Raza, N., Javid, A.: Optical dark and dark-singular soliton solutions of (1+2)-dimensional Chiral Nonlinear Schrödinger equation. Waves Random Complex Media 29, 496–508 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  • Raza, N., Abdullah, M., Butt, A.R., Murtaza, I.G., Sial, S.: New exact periodic elliptic wave solutions for extended quantum Zakharov–Kuznetsov equation. Opt. Quant. Electron. 50(4), 177 (2018)

    Article  Google Scholar 

  • Rehman, S.U., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Sulaiman, T.A., Yusuf, A.: Modulation instability analysis and optical solitons of the generalized model for description of propagation pulses in optical fiber with four non-linear terms. Mod. Phys. Lett. B 35, 2150112 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  • Rezazadeh, H., Korkmaz, A., Eslami, M., Vahidi, J., Asghari, R.: Traveling wave solution of conformable fractional generalized reaction doffing model by generalized projective Riccati equation method. Opt. Quantum Electron. 50, 150 (2018)

    Article  Google Scholar 

  • Ryabov, P.N., Sinelshchikov, D.I., Kochanov, M.B.: Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations. Appl. Math. Comput. 218, 3965–3972 (2011)

    MathSciNet  MATH  Google Scholar 

  • Saha, A., Ali, K.K., Rezazadeh, H., Ghatani, Y.: Analytical optical pulses and bifurcation analysis for the traveling optical pulses of the hyperbolic nonlinear Schrödinger equation. Opt. Quantum Electron. 53, 150 (2021)

    Article  Google Scholar 

  • Seadawy, A.R., Ali, K.A.: Jian-Guo Liu, New optical soliton solutions for Fokas-Lenells dynamical equation via two various methods. Modern Phys. Lett. B (2021). https://doi.org/10.1142/S0217984921501967

    Article  Google Scholar 

  • Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R.: Resonant optical solitons with conformable time-fractional nonlinear Schrödinger equation. Int. J. Mod. Phys. B 35, 2150044 (2021)

    Article  ADS  MATH  Google Scholar 

  • Senol, M., Akinyemi, L., Ata, A., Iyiola, O.S.: Approximate and generalized solutions of conformable type Coudrey–Dodd–Gibbon–Sawada–Kotera equation. Int. J. Mod. Phys. B 35, 2150021 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Tchier, F., Aslan, E.C., Inc, M.: Optical solitons in parabolic law medium: Jacobi elliptic function solution. Nonlinear Dyn. 85, 2577–2582 (2016)

    Article  MathSciNet  Google Scholar 

  • Usman, A., Raza, N., Murtaza, I.G.: On soliton solutions of time fractional form of Sawada–Kotera equation. Nonlinear Dyn. 95(1), 391–405 (2019)

    Article  MATH  Google Scholar 

  • Yan, C.T.: A simple transformation for nonlinear waves. Phys. Lett. A 224, 77–84 (1996)

  • Younas, U., Younis, M., Seadawy, A.R., Rizvi, S.T.R., Althobaiti, S.: Samy Sayed, Diverse exact solutions for modified nonlinear Schrödinger equation with conformable fractional derivative are constructed. Res. Phys. 20, 103766 (2021)

  • Younas, B., Younis, M.: Chirped solitons in optical monomode fibres modelled with Chen-Lee-Liu equation. Pramana-J. Phys. 3, 94 (2020)

    Google Scholar 

  • Yu, W., Ekici, M., Mirzazadeh, M., Zhou, Q., Liu, W.: Periodic oscillation of dark solitons in nonlinear optics. Optik 165, 341–344 (2018)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, AL-Azhar University, Nasr City, P. N. Box: 11884, Cairo, Egypt

    Khalid K. Ali

  2. Department of Mechanical Engineering, Ahrar Institute of Technology and Higher Education, Rasht, Iran

    Ali Zabihi

  3. Faculty of Modern Technologies Engineering, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

  4. Department of Mechanical Engineering, University of Guilan, Rasht, Iran

    Reza Ansari

  5. Department of Computer Engineering, Biruni University, Istanbul, Turkey

    Mustafa Inc

  6. Sience Faculty, Department of Mathematics, Firat University, 23119, Elazig, Turkey

    Mustafa Inc

  7. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Mustafa Inc

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  1. Khalid K. Ali
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  2. Ali Zabihi
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  3. Hadi Rezazadeh
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  4. Reza Ansari
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  5. Mustafa Inc
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Ali, K.K., Zabihi, A., Rezazadeh, H. et al. Optical soliton with Kudryashov’s equation via sine-Gordon expansion and Kudryashov methods. Opt Quant Electron 53, 362 (2021). https://doi.org/10.1007/s11082-021-02998-6

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