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The higher-order nonlinear Schrödinger’s dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity via dispersive analytical soliton wave solutions

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Abstract

In this work, we utilize the extended simplest equation method to obtain exact solutions for the higher-order nonlinear Schrödinger’s equation with fourth-order dispersion and cubic-quintic nonlinearity that describe the propagation of extremely short pulses in optical fibers. With the aid of this method, we get many exact solutions like singular-bright combo soliton solutions, bright, dark and singular soliton solutions, periodic solutions and other solutions. Moreover, for the physical illustration of the obtained solutions, 3D and 2D graphs are presented.

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References

  • Al-Amr, M.O., El-Ganaini, S.: New exact traveling wave solutions of the (4+1)-dimensional Fokas equation. Comput. Math. Appl. 74, 1274–1287 (2017)

    Article  MathSciNet  Google Scholar 

  • Alamri, S.Z., Seadawy, A.R., Al-Sharari, H.M.: Study of optical soliton fibers with power law model by means of higher-order nonlinear Schrödinger dynamical system. Results Phys. 13, 102251 (2019)

    Article  Google Scholar 

  • Aly, R.: Seadawy, exact Solutions of a two-dimensional nonlinear Schrodinger equation. Appl. Math. Lett. 25, 687–691 (2012)

    Article  MathSciNet  Google Scholar 

  • Arshad, M., Seadawy, A.R., Lu, D.: Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications. Superlatt. Microstruct. 112, 422–434 (2017)

    Article  ADS  Google Scholar 

  • Arshad, M., Seadawy, A.R., Lua, D.: Exact bright-dark solitary wave solutions of the higher-order cubic-quintic nonlinear Schrödinger equation and its stability. Optics 138, 40–49 (2017)

    ADS  Google Scholar 

  • Arshad, M., Seadawy, A.R., Lua, D.: Elliptic function and solitary wave solutions of the higher-order nonlinear Schr\(\ddot{o}\)dinger dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity and its stability. Eur. Phys. J. Plus 132, 371 (2017)

    Article  Google Scholar 

  • Arshad, M., Seadawy, A., Lu, D.: Optical soliton solutions of the generalized higher-order nonlinear Schrodinger equations and their applications. Opt. Quantum Electr. 49(421), 1–16 (2017)

    Google Scholar 

  • Bhatti, M. M., Lu, D. Q.: An application of Nwogu’s Boussinesq model to analyze the head-on collision process between hydroelastic solitary waves. Open Phys. 17(1), 177–191 (2019)

  • Bhatti, M. M., Lu, D. Q.: Hydroelastic solitary wave during the head-on collision process in a stratified fluid, Proceedings of the Institution of Mechanical Engineers, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 233, 17, pp. 6135–6148 (2019)

  • Bhatti, M.M., Lu, D.Q.: Analytical study of the head-on collision process between hydroelastic solitary waves in the presence of a uniform current. Symmetry 11(3), 333 (2019)

    Article  Google Scholar 

  • Bilige, S., Chaolu, T., Wang, X.: Application of the extended simplest equation method to the coupled Schrödinger–Boussinesq equation. Appl. Math. Comput. 244, 517–523 (2013)

    MATH  Google Scholar 

  • Chen, S.J., Lin, J.N., Wang, Y.Y.: Soliton solutions and their stabilities of three (2+ 1)-dimensional PT-symmetric nonlinear Schrödinger equations with higher-order diffraction and nonlinearities. Optik. 194, 162753 (2019)

    Article  ADS  Google Scholar 

  • Darvishi, M. T., Najafi, M., Seadawy, A. R.: Dispersive bright, dark and singular optical soliton solutions in conformable fractional optical fiber Schrodinger models and its applications, Opt. Quantum Electr., 50 (2018) 181, 1–16

  • El-Sheikh, M.M.A., Ahmed, H.M., Arnous, A.H., Rabie, W.B.: Optical solitons with the differential group delay for coupled Kundu–Eckhaus equation using extended simplest equation approach. Optik 208, 164051 (2020)

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  • Javid, A., Seadawy, A.R., Raza, N.: Dual-wave of resonant nonlinear Schrödinger’s dynamical equation with different nonlinearities. Phys. Lett. A 407, 127446 (2021)

  • Jhangeera, A., Raza, N., Rezazadeh, H., Seadawy, A.: Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model, Pramana volume 94. Article number 87,(2020)

  • 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)

    Article  Google Scholar 

  • Raza, N., Seadawy, A.R., Kaplan, M., Butt, A.R.: Symbolic computation and sensitivity analysis of nonlinear Kudryashov’s dynamical equation with applications. Phys. Scripta 96, 105216 (2021)

  • Raza, N., ur Rahman, R., Seadawy, A., Jhangeer, A.: Computational and bright soliton solutions and sensitivity behavior of Camassa-Holm and nonlinear Schrodinger dynamical equation, Int. J. Mod. Phys. B, 35(11), 2150157 (2021)

  • Raza, N., Sial, S., Siddiqi, S.S., Lookmand, T.: Energy minimization related to Nonlinear Schrodinger equation. J. Comput. Phys. 228, 2572–2577 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  • Raza, N., Jhangeer, A., Seadawy, A.R., Butt, A.R., Arshed, S.: Dynamical behavior of micro-structured solids with conformable time fractional strain wave equation. Phys. Lett. A 384, 126683 (2020)

    Article  MathSciNet  Google Scholar 

  • Raza, N., Hassan, Z., Seadawy, A.: Computational Soliton solutions for the variable coefficient nonlinear Schrödinger equation by collective variable method. Opt. Quantum Electr. 53, 400 (2021)

    Article  Google Scholar 

  • Razzaq, A., Seadawy, A.R., Raza, N.: Heat transfer analysis of viscoelastic fluid flow with fractional Maxwell model in the cylindrical geometry. Phys. Scripta 95, 115220 (2020)

    Article  ADS  Google Scholar 

  • Seadawy, A.: The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrodinger equation and its solutions. Optik - Int. J. Light Electron Opt. 139, 31–43 (2017)

  • Seadawy, A.R.: Approximation solutions of derivative nonlinear Schrodinger equation with computational applications by variational method. Eur. Phys. J. Plus 130(182), 1–10 (2015)

    Google Scholar 

  • Seadawy, A.R.: Modulation instability analysis for the generalized derivative higher order nonlinear Schrödinger equation and its the bright and dark soliton solutions. J. Electromagn. Waves Appl. 31, 1353–1362 (2017)

    Article  MathSciNet  Google Scholar 

  • Seadawy, A.R., Ahmed, H.M., Rabie, W.B., Biswas, A.: Chirp-free optical solitons in fiber Bragg gratings with dispersive reflectivity having polynomial law of nonlinearity. Optics 225, 165681 (2021)

    ADS  Google Scholar 

  • Tariq, K.U., Seadawy, A.R., Younis, M.: Explicit, Periodic and dispersive optical soliton solutions to the generalized nonlinear Schrodinger dynamical equation with higher order dispersion and cubic-quintic nonlinear terms. Opt. Quantum Electr. 50(163), 1–19 (2018)

    Google Scholar 

  • Xu, B., Yan, M., Sun, Z., Tong, X.: Optical solitons of the (1+ 1)-dimensional higher-order nonlinear Schrödinger equations with PT-symmetric potentials. Optik. 181, 1019–1022 (2019)

    Article  ADS  Google Scholar 

  • Zayed, E.M.E., Shohib, R.M.A.: Optical solitons and other solutions to Biswas–Arshed equation using the extended simplest equation method. Opt. 185, 626–635 (2019)

    Google Scholar 

  • Zhang, J., Chaoqingi, D.: Bright and dark optical solitons in the nonlinear Schrodinger equation with fourth-order dispersion and cubic-quintic nonlinearity. Chinese Opt. Lett. 3, 295–298 (2005)

    ADS  Google Scholar 

  • Zhang, J.F., Dai, C.Q.: Bright and dark optical solitons in the nonlinear Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity. Chin. Opt. 3, 295–298 (2005)

    Google Scholar 

  • Zhang, Q., Xiong, M., Chen, L., et al.: Exact travelling wave solutions of two nonlinear schrödinger equations by using two methods. J. Appl. Math. Phys. 7, 3101 (2019)

    Article  Google Scholar 

  • Zhou, Q., Zhu, Q.: Optical solitons in medium with parabolic law nonlinearity and higher order dispersion. Waves Random Complex Media 25, 52–59 (2015)

    Article  ADS  Google Scholar 

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Acknowledgements

Taif University Researchers Supporting Project number (TURSP-2020/326), Taif University, Taif, Saudi Arabia.

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Authors and Affiliations

  1. Department of Physics and Engineering Mathematics, Higher Institute of Engineering and Technology, Tanta, Egypt

    Wafaa B. Rabie

  2. Department of Physics and Engineering Mathematics, Higher Institute of Engineering El Shorouk Academy, El-Shorouk City, Cairo, Egypt

    Hamdy M. Ahmed

  3. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Aly R. Seadawy

  4. Mathematics Department, College of Science, Taif University, P.O. Box 11099, Taif , 21944, Saudi Arabia

    Ali Althobaiti

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  1. Wafaa B. Rabie
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  2. Hamdy M. Ahmed
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  3. Aly R. Seadawy
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  4. Ali Althobaiti
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Correspondence to Aly R. Seadawy.

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Rabie, W.B., Ahmed, H.M., Seadawy, A.R. et al. The higher-order nonlinear Schrödinger’s dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity via dispersive analytical soliton wave solutions. Opt Quant Electron 53, 668 (2021). https://doi.org/10.1007/s11082-021-03278-z

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