Novel solitons through optical fibres for perturbed cubic-quintic-septic nonlinear Schr\"{o}dinger-type equation

Document Type : Research Paper

Authors

1 Department of Mathematics and Statistics, Faculty of Science, Mutah University, AlKarak, Jordan

2 Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Kuala Terengganu, Malaysia

3 Preparatory Year, Saudi Electronic University, Abha, Kingdom of Saudi Arabia

4 Department of Mathematics, Lafayette College, Easton, Pennsylvania, USA

5 Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

Abstract

The current analysis employs the Riccati and modified simple equation methods to retrieve new optical solitons for highly dispersive nonlinear Schr\"{o}dinger-type equation (NLSE). With cubic-quintic-septic law (also known as a polynomial) of refractive index and perturbation terms having cubic nonlinearity, 1-optical solitons in the form of hyperbolic, periodic, and rational are derived. the two schemes offer an influential mathematical tool for solving NLSEs in various areas of applied sciences.

Keywords

[1] T. Abdeljawad, On conformable fractional calculus. J. Comput. Appl. Math. 279 (2015) 57-–66.[2] M.A. Abdou, On the fractional order space-time nonlinear equations arising in plasma physics, Indian J. Phys. 93(4) (2019) 537–541.
[3] M.A. Akbar, L. Akinyemi, S.W. Yao, A. Jhangeer, H. Rezazadeh, M.M. Khater, H. Ahmad and M. Inc, Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method, Res. Phys. 25 (2021) 104228.
[4] L. Akinyemi, q-Homotopy analysis method for solving the seventh-order time-fractional Lax’s Korteweg–de Vries and Sawada–Kotera equations, Comp. Appl. Math. 38(4) (2019) 1–22.
[5] L. Akinyemi, O.S. Iyiola and U. Akpan, Iterative methods for solving fourth- and sixth-order time-fractional Cahn-Hillard equation, Math. Meth. Appl. Sci. 43(7) (2020) 4050—4074.
[6] L. Akinyemi, M. Senol and O.S. Iyiola, Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method, Math. Comput. Simul. 182 (2021) 211–233.
[7] L. Akinyemi, M. Senol and S.N. Huseen, Modified homotopy methods for generalized fractional perturbed Zakharov Kuznetsov equation in dusty plasma, Adv. Differ. Equ. 2021(1) (2021) 1–27.
[8] L. Akinyemi and O.S. Iyiola, Exact and approximate solutions of time-fractional models arising from physics via Shehu transform, Math. Meth. Appl. Sci. 43(12) (2020) 7442–7464.
[9] L. Akinyemi and O.S. Iyiola, A reliable technique to study nonlinear time-fractional coupled Korteweg-de Vries equations, Adv. Differ. Equ. 2020 (2020) 1–27.
[10] E.A. Az-Zo’bi, A reliable analytic study for higher-dimensional telegraph equation, J. Math. Comput. Sci. 18 (2018) 423—429.
[11] E.A. Az-Zo’bi, A. Yıldırım and W.A. AlZoubi, The residual power series method for the one-dimensional unsteady flow of a van der Waals gas, Physica A 517 (2019) 188—196.
[12] E.A. Az-Zo’bi, Exact Analytic Solutions for Nonlinear Diffusion Equations via Generalized Residual Power Series Method, International J. Math. Comput. Sci. 14(1) (2019) 69–78.
[13] E.A. Az-Zo’bi, New kink solutions for the van der Waals p-system, Math. Meth. Appl. Sci. 42(18) (2019) 6216–6226.
[14] E.A. Az-Zo’bi, Peakon and solitary wave solutions for the modified Fornberg-Whitham equation using simplest equation method, International J. Math. Comput. Sci. 14(3) (2019) 635–645.
[15] E.A. Az-Zobi, Modified Laplace decomposition method, World Appl. Sci. J. 18(11) (2012) 1481–1486.
[16] E.A. Az-Zobi, An Approximate Analytic Solution for Isentropic Flow by An Inviscid Gas Equations, Arch. Mech. 66(3) (2014) 203–212.
[17] E.A. Az-Zobi, Construction of Solutions for Mixed Hyperbolic Elliptic Riemann Initial Value System of Conservation Laws, Appl. Math. Model. 37 (2013) 6018–6024.
[18] E.A. Az-Zobi, K. Al-Khaled and A. Darweesh, Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method, Math. 7 (2019) 550.
[19] E.A. Az-Zobi, K. Al Dawoud, M.F. Marashdeh, Numeric-analytic solutions of mixed-type systems of balance laws, Appl. Math. Comput. 265 (2015) 133—143.
[20] E.A. Az-Zobi, On the reduced differential transform method and its application to the generalized Burgers-Huxley equation, Appl. Math. Sci. 8 (177) (2014) 8823—8831.
[21] E.A. Az-Zobi, M.O. Al-Amr, A. Yıldırım and W.A. AlZoubi, Revised reduced differential transform method using Adomian’s polynomials with convergence analysis, Math. Engin. Sci. Aerospace 11(4) (2020) 827–840.
[22] E.A. Az-Zobi, L. Akinyemi and A.O. Alleddawi, Construction of optical solitons for the conformable generalized model in nonlinear media, Modern Physics Letters B 35(24) (2021) 2150409.
[23] E.A. Az-Zobi, W.A. Alzoubi, L. Akinyemi, M. S¸enol and B.S. Masaedeh, A variety of wave amplitudes for the conformable fractional (2 + 1)-dimensional Ito equation, Modern Phys. Lett. B 35(15) (2021) 2150254.
[24] E.A. Az-Zobi, W.A. AlZoubi, L. Akinyemi, M. S¸enol, I.W. Alsaraireh and M. Mamat, Abundant closed-form solitons for time-fractional integro–differential equation in fluid dynamics, Opt. Quant. Electron. 53 (2021) 132.
[25] A. Boukhouima, K. Hattaf, E.M. Lotfi, M. Mahrouf, D.F. Torres and N. Yousfi, Lyapunov functions for fractionalorder systems in biology: Methods and applications, Chaos, Solitons Fractals 140 (2020) 110224.
[26] A. Biswas, M. Ekici, A. Sonomezoglu and M. Belic, Highly dispersive optical solitons with cubic-quintic–septic law by exp-expansion, Optik 186 (2019) 321—325.
[27] A. Biswas, M. Ekici, A. Sonomezoglu and M. Belic, Highly dispersive optical solitons with cubic–quintic–septic law by extended Jacobi’s elliptic function expansion, Optik 183 (2019) 571—578.
[28] A. Biswas, M. Ekici, A. Sonomezoglu and M. Belic, Highly dispersive optical solitons with cubic-quintic–septic law by F-expansion, Optik 182 (2019) 897–906.
[29] A. Biswas, Optical soliton perturbation with Radhakrishnan–Kundu–Laksmanan equation by traveling wave hypothesis, Optik 171 (2018) 217–220.
[30] A. Biswas, M. Ekici, A. Sonmezoglu and M.R. Belic, Highly dispersive optical solitons with cubic–quintic–septic law by extended Jacobi’s elliptic function expansion, Optik 183 (2019) 571-–578.
[31] A. Biswas, M. Ekici, A. Sonmezoglu and M.R. Belic, Highly dispersive optical solitons with cubic–quintic–septic law by exp-expansion, Optik, 186 (2019) 321–325. https://doi.org/10.1016/j.rinp.2020.103021.
[32] A. Biswas, A.H. Kara, Q. Zhou, A.K. Alzahrani and M.livoj R. Belic, Conservation laws for highly dispersive optical Solitons in birefringent fibers, Regul. Chaot. Dyn. 25 (2020) 166-–177.
[33] M. Ekici and A. Sonmezoglu, Optical solitons with Biswas–Arshed equation by extended trial function method, Optik 177 (2019) 13–20.
[34] B. Ghanbari, M.S. Osman and D. Baleanu, Generalized exponential rational function method for extended Zakharov–Kuznetsov equation with conformable derivative, Modern Phys. Lett. A 34(20) (2019) 1950155.
[35] O. Gonz´alez-Gaxiola, A. Biswas, A.K. Alzahrani and M.R. Belic, Highly dispersive optical solitons with a polynomial law of refractive index by Laplace–Adomian decomposition, J. Comput. Electron. 20 (2021) 1216—1223.
[36] J.H. He and F.Y. Ji, Two-scale mathematics and fractional calculus for thermodynamics, Thermal Sci. 23(4) (2019) 2131–2133.
[37] S.J. Johnston, H. Jafari, S.P. Moshokoa, V.M. Ariyan and D. Baleanu, Laplace homotopy perturbation method for Burgers equation with space-and time-fractional order, Open Phys. 14(1) (2016) 247–252.
[38] R. Khalil, Al M. Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014) 65–70.
[39] R.W. Kohl, A. Biswas, M. Ekici, Q. Zhou, S. Khan, A.S. Alshomrani and M.R. Belic, Highly dispersive optical soliton perturbation with cubic–quintic–septic refractive index by semi-inverse variational principle, Optik 199 (2019) 163322.
[40] R.W. Kohl, A. Biswas, M. Ekici, Q. Zhou, S. Khan, A.S. Alshomrani and M.R. Belic, Highly dispersive optical soliton perturbation with cubic–quintic–septic refractive index by semi-inverse variational principle, Optik 199 (2019) 163322. https://doi.org/10.1016/j.ijleo.2019.163322
[41] R.W. Kohl, A. Biswas, M. Ekici, Q. Zhou, S. Khan, A.S. Alshomrani and M.R. Belic, Sequel to highly dispersive optical soliton perturbation with cubic-quintic-septic refractive index by semi-inverse variational principle, Optik 203 (2020) 163451. https://doi.org/10.1016/j.ijleo.2019.163451
[42] O. Kolebaje, E. Bonyah and L. Mustapha, The first integral method for two fractional non-linear biological models, Discrete Continuous Dynamical Syst. 12(3) (2019) 487.
[43] N.A. Kudryashov, First integrals and general solutions of the Biswas–Milovic equation, Optik 210 (2020) 164490.
[44] A. Kurt, A. Tozar and O.Tasbozan Applying the new extended direct algebraic method to solve the equation of obliquely interacting waves in shallow waters, J. Ocean Univ. China 19(4) (2020) 772–780.
[45] A. Kumar, R. Komaragiri and M. Kumar, Design of efficient fractional operator for ECG signal detection in implantable cardiac pacemaker systems, Int. J. Circuit Theory Appl. 47(9) (2019) 1459–1476.
[46] M.S. Osman, A. Korkmaz, H. Rezazadeh, M. Mirzazadeh, M. Eslami and Q. Zhou, The unified method for conformable time-fractional Schrodinger equation with perturbation terms, Chinese J. Phys. 56(5) (2018) 2500–2506.
[47] I. Owusu-Mensah, L. Akinyemi, B. Oduro and O.S. Iyiola, A fractional order approach to modeling and simulations of the novel COVID-19, Adv. Differ. Equ. 2020(1) (2020) 1–21.
[48] E. Pellegrino, L. Pezza and F. Pitolli, A collocation method in spline spaces for the solution of linear fractional dynamical systems, Math. Comput. Simulat. 176 (2020) 266–278.
[49] N.M. Rasheed, M.O. Al-Amr, E.A. Az-Zo’bi, M.A. Tashtoush and L. Akinyemi, Stable optical solitons for the higher-order Non-Kerr NLSE via the modified simple equation method, Math. 9 (2021) 1986.
[50] A.R. Seadawy, K.K. Ali and R.I. Nuruddeen, A variety of soliton solutions for the fractional Wazwaz-BenjaminBona Mahony equations, Results Phys. 12 (2019) 2234–2241.
[51] M. Senol, New analytical solutions of fractional symmetric regularized-long-wave equation, Revista Mexic. F´ıs. 66(3 May-Jun) (2020) 297–307.
[52] M. Senol, O.S. Iyiola, H. Daei Kasmaei and L. Akinyemi, Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent-Miodek system with energy-dependent Schr¨odinger potential. Adv. Differ. Equ. 2019 (2019) 1–21.
[53] M. Senol, Analytical and approximate solutions of (2 + 1)-dimensional time-fractional Burgers-KadomtsevPetviashvili equation, Commun. Theor. Phys. 72(5) (2020) 1–11.
[54] H.M. Srivastava, D. Baleanu, J.A.T. Machado, M.S. Osman, H. Rezazadeh, S. Arshed and H. Gunerhan, Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method, Physica Scripta 95 (2020) 075217.
[55] O. Tasbozan, Y. C¸ enesiz, A. Kurt and D. Baleanu, New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method, Open Phys. 15(1) (2017) 647–651.
[56] N. Ullah, H.U. Rehman, M.A. Imran and T. Abdeljawad, Highly dispersive optical solitons with cubic law and cubic-quintic-septic law nonlinearities, Res. Phys. 17 (2020) 103021.
[57] G. Wang, Y. Liu, Y. Wu and X. Su, Symmetry analysis for a seventh-order generalized KdV equation and its fractional version in fluid mechanics, Fractals 28(3) (2020) 2050044–134.
[58] E.M.E. Zayed, M.E.M. Alngar, M.M. El-Horbaty, A. Biswas, M. Ekici, A.S. Alshomrani, S. Khan, Q. Zhou and M.R. Belic, Optical solitons in birefringent fibers having anti-cubic nonlinearity with a few prolific integration algorithms, Optik 200 (2020) 163229.
[59] E.M.E. Zayed, M.E.M. Alngar, M.M. El-Horbaty, A. Biswas, M. Ekici, Q. Zhou, S. Khan, F. Mallawi and M.R. Belic, Highly dispersive optical solitons in the nonlinear Schr¨odinger’s equation having polynomial law of the refractive index change, Indian J. Phys. 95 (2021) 109—119.
Volume 13, Issue 1
March 2022
Pages 1493-1506
  • Receive Date: 06 April 2021
  • Revise Date: 08 June 2021
  • Accept Date: 20 June 2021