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Published in: Optical and Quantum Electronics 1/2024

01-01-2024

Extraction of optical solitons for nonlinear Biswas–Milovic equation in magneto-optic waveguide

Authors: Tahir Shahzad, Muhammad Zafarullah Baber, Tukur Abdulkadir Sulaiman, Muhammad Ozair Ahmad, Nauman Ahmed

Published in: Optical and Quantum Electronics | Issue 1/2024

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Abstract

In this study, the optical soliton solutions are extracted for the nonlinear Biswas–Milovic equation. The Biswas–Milovic equation is a coupled system in magneto-optic waveguide having Kudryashov’s law of refractive index. These equations have many applications in different branches of science, telecommunication industry, and technology. The exact optical soliton solutions are obtained by applying the \(\phi ^6\)-model expansion approach. This approach provides us the solutions in the form of Jacobi elliptic function, such as hyperbolic function solutions and trigonometric function solutions. The solutions are obtained in the form of dark soliton, bright soliton, periodic soliton, and singular soliton. Symbolic computations were used to validate all of the solutions obtained. In addition, some selected solutions are graphically described to demonstrate the physical characteristics of the gained solutions.

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Literature
go back to reference Ablowitz, M.J., Clarkson, P.A.: Solitons, nonlinear evolution equations and inverse scattering, vol. 149. Cambridge University Press, Cambridge (1991)CrossRef Ablowitz, M.J., Clarkson, P.A.: Solitons, nonlinear evolution equations and inverse scattering, vol. 149. Cambridge University Press, Cambridge (1991)CrossRef
go back to reference Baskonus, H.M., Bulut, H.: Analytical studies on the (1+ 1)-dimensional nonlinear dispersive modified Benjamin–Bona–Mahony equation defined by seismic sea waves. Waves Random Complex Media 25(4), 576–586 (2015)MathSciNetCrossRefADS Baskonus, H.M., Bulut, H.: Analytical studies on the (1+ 1)-dimensional nonlinear dispersive modified Benjamin–Bona–Mahony equation defined by seismic sea waves. Waves Random Complex Media 25(4), 576–586 (2015)MathSciNetCrossRefADS
go back to reference Biswas, A.: Solitons in magneto-optic waveguides. Appl. Math. Comput. 153(2), 387–393 (2004)MathSciNet Biswas, A.: Solitons in magneto-optic waveguides. Appl. Math. Comput. 153(2), 387–393 (2004)MathSciNet
go back to reference Biswas, A., Milovic, D.: Bright and dark solitons of the generalized nonlinear Schrödinger’s equation. Commun. Nonlinear Sci. Numer. Simul. 15(6), 1473–1484 (2010)MathSciNetCrossRefADS Biswas, A., Milovic, D.: Bright and dark solitons of the generalized nonlinear Schrödinger’s equation. Commun. Nonlinear Sci. Numer. Simul. 15(6), 1473–1484 (2010)MathSciNetCrossRefADS
go back to reference Biswas, A., Jawad, A.J.A.M., Manrakhan, W.N., Sarma, A.K., Khan, K.R.: Optical solitons and complexitons of the Schrödinger-Hirota equation. Opt. Laser Technol. 44(7), 2265–2269 (2012)CrossRefADS Biswas, A., Jawad, A.J.A.M., Manrakhan, W.N., Sarma, A.K., Khan, K.R.: Optical solitons and complexitons of the Schrödinger-Hirota equation. Opt. Laser Technol. 44(7), 2265–2269 (2012)CrossRefADS
go back to reference Crutcher, S.H., Osei, A.: The modulated spatial Gausson solution to the Biswas–Milovic equation with log law nonlinearity. Optik 124(20), 4678–4681 (2013)CrossRefADS Crutcher, S.H., Osei, A.: The modulated spatial Gausson solution to the Biswas–Milovic equation with log law nonlinearity. Optik 124(20), 4678–4681 (2013)CrossRefADS
go back to reference Dai, C.Q., Zhou, G.Q., Zhang, J.F.: Controllable optical rogue waves in the femtosecond regime. Phys. Rev. E 85(1), 016603 (2012)CrossRefADS Dai, C.Q., Zhou, G.Q., Zhang, J.F.: Controllable optical rogue waves in the femtosecond regime. Phys. Rev. E 85(1), 016603 (2012)CrossRefADS
go back to reference Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83, 731–738 (2016)MathSciNetCrossRef Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83, 731–738 (2016)MathSciNetCrossRef
go back to reference Iqbal, M.S., Seadawy, A.R., Baber, M.Z.: Demonstration of unique problems from soliton solutions to nonlinear Selkov-Schnakenberg system. Chaos, Solitons Fractals 162, 112485 (2022)MathSciNetCrossRef Iqbal, M.S., Seadawy, A.R., Baber, M.Z.: Demonstration of unique problems from soliton solutions to nonlinear Selkov-Schnakenberg system. Chaos, Solitons Fractals 162, 112485 (2022)MathSciNetCrossRef
go back to reference Kaur, L., Wazwaz, A.M.: Bright-dark optical solitons for Schrödinger-Hirota equation with variable coefficients. Optik 179, 479–484 (2019)CrossRefADS Kaur, L., Wazwaz, A.M.: Bright-dark optical solitons for Schrödinger-Hirota equation with variable coefficients. Optik 179, 479–484 (2019)CrossRefADS
go back to reference Kudryashov, N.A.: Mathematical model of propagation pulse in optical fiber with power nonlinearities. Optik 212, 164750 (2020)CrossRefADS Kudryashov, N.A.: Mathematical model of propagation pulse in optical fiber with power nonlinearities. Optik 212, 164750 (2020)CrossRefADS
go back to reference Kumar, S., Malik, S., Biswas, A., Zhou, Q., Moraru, L., Alzahrani, A.K., Belic, M.R.: Optical solitons with Kudryashov’s equation by Lie symmetry analysis. Phys. Wave Phenom. 28, 299–304 (2020)CrossRefADS Kumar, S., Malik, S., Biswas, A., Zhou, Q., Moraru, L., Alzahrani, A.K., Belic, M.R.: Optical solitons with Kudryashov’s equation by Lie symmetry analysis. Phys. Wave Phenom. 28, 299–304 (2020)CrossRefADS
go back to reference Malik, S., Kumar, S.: Pure-cubic optical soliton perturbation with full nonlinearity by a new generalized approach. Optik 258, 168865 (2022)CrossRefADS Malik, S., Kumar, S.: Pure-cubic optical soliton perturbation with full nonlinearity by a new generalized approach. Optik 258, 168865 (2022)CrossRefADS
go back to reference Malik, S., Kumar, S., Biswas, A., Yildirim, Y., Moraru, L., Moldovanu, S., Alshehri, H.M.: Cubic-quartic optical solitons in fiber bragg gratings with dispersive reflectivity having parabolic law of nonlinear refractive index by lie symmetry. Symmetry 14(11), 2370 (2022)CrossRefADS Malik, S., Kumar, S., Biswas, A., Yildirim, Y., Moraru, L., Moldovanu, S., Alshehri, H.M.: Cubic-quartic optical solitons in fiber bragg gratings with dispersive reflectivity having parabolic law of nonlinear refractive index by lie symmetry. Symmetry 14(11), 2370 (2022)CrossRefADS
go back to reference Malik, S., Kumar, S., Biswas, A., Yildirim, Y., Moraru, L., Moldovanu, S., Alotaibi, A.: Gap solitons in fiber bragg gratings having polynomial law of nonlinear refractive index and cubic-quartic dispersive reflectivity by lie symmetry. Symmetry 15(5), 963 (2023)CrossRefADS Malik, S., Kumar, S., Biswas, A., Yildirim, Y., Moraru, L., Moldovanu, S., Alotaibi, A.: Gap solitons in fiber bragg gratings having polynomial law of nonlinear refractive index and cubic-quartic dispersive reflectivity by lie symmetry. Symmetry 15(5), 963 (2023)CrossRefADS
go back to reference Manafian, J.: On the complex structures of the Biswas–Milovic equation for power, parabolic and dual parabolic law nonlinearities. Eur. Phys. J. Plus 130(12), 255 (2015)CrossRef Manafian, J.: On the complex structures of the Biswas–Milovic equation for power, parabolic and dual parabolic law nonlinearities. Eur. Phys. J. Plus 130(12), 255 (2015)CrossRef
go back to reference Rehman, H.U., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Anwar, I., Baber, M.Z., Althobaiti, A.: Weakly nonlinear electron-acoustic waves in the fluid ions propagated via a (3+ 1)-dimensional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation in plasma physics. Results Phys. 33, 105069 (2022)CrossRef Rehman, H.U., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Anwar, I., Baber, M.Z., Althobaiti, A.: Weakly nonlinear electron-acoustic waves in the fluid ions propagated via a (3+ 1)-dimensional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation in plasma physics. Results Phys. 33, 105069 (2022)CrossRef
go back to reference Rezazadeh, H., Mirhosseini-Alizamini, S.M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger-Hirota equation. Optik 172, 545–553 (2018)CrossRefADS Rezazadeh, H., Mirhosseini-Alizamini, S.M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger-Hirota equation. Optik 172, 545–553 (2018)CrossRefADS
go back to reference Seadawy, A.R., Younis, M., Baber, M.Z., Rizvi, S.T., Iqbal, M.S.: Diverse acoustic wave propagation to confirmable time-space fractional KP equation arising in dusty plasma. Commun. Theor. Phys. 73(11), 115004 (2021)MathSciNetCrossRefADS Seadawy, A.R., Younis, M., Baber, M.Z., Rizvi, S.T., Iqbal, M.S.: Diverse acoustic wave propagation to confirmable time-space fractional KP equation arising in dusty plasma. Commun. Theor. Phys. 73(11), 115004 (2021)MathSciNetCrossRefADS
go back to reference Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique. Chaos, Solitons Fractals 144, 110669 (2021)MathSciNetCrossRef Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique. Chaos, Solitons Fractals 144, 110669 (2021)MathSciNetCrossRef
go back to reference Seadawy, A.R., Younis, M., Iqbal, M.S., Baber, M.Z., Rizvi, S.T., Raheem, A.: Soliton behavior of algae growth dynamics leading to the variation in nutrients concentration. J. King Saud Univ. Sci. 34(5), 102071 (2022)CrossRef Seadawy, A.R., Younis, M., Iqbal, M.S., Baber, M.Z., Rizvi, S.T., Raheem, A.: Soliton behavior of algae growth dynamics leading to the variation in nutrients concentration. J. King Saud Univ. Sci. 34(5), 102071 (2022)CrossRef
go back to reference Seadawy, A.R., Younis, M., Iqbal, M.S., Baber, M.Z., Rizvi, S.T., Raheem, A.: Soliton behavior of algae growth dynamics leading to the variation in nutrients concentration. J. King Saud Univ. Sci. 34(5), 102071 (2022)CrossRef Seadawy, A.R., Younis, M., Iqbal, M.S., Baber, M.Z., Rizvi, S.T., Raheem, A.: Soliton behavior of algae growth dynamics leading to the variation in nutrients concentration. J. King Saud Univ. Sci. 34(5), 102071 (2022)CrossRef
go back to reference Shahzad, T., Ahmad, M.O., Baber, M.Z., Ahmed, N., Ali, S.M., Akgül, A., Eldin, S.M.: Extraction of soliton for the confirmable time-fractional nonlinear Sobolev-type equations in semiconductor by ϕ6-modal expansion method. Results Phys. 46, 106299 (2023)CrossRef Shahzad, T., Ahmad, M.O., Baber, M.Z., Ahmed, N., Ali, S.M., Akgül, A., Eldin, S.M.: Extraction of soliton for the confirmable time-fractional nonlinear Sobolev-type equations in semiconductor by ϕ6-modal expansion method. Results Phys. 46, 106299 (2023)CrossRef
go back to reference Soliman, A.A., Abdo, H.A.: New exact Solutions of nonlinear variants of the RLW, the PHI-four and Boussinesq equations based on modified extended direct algebraic method. (2012). arXiv preprint arXiv:1207.5127 Soliman, A.A., Abdo, H.A.: New exact Solutions of nonlinear variants of the RLW, the PHI-four and Boussinesq equations based on modified extended direct algebraic method. (2012). arXiv preprint arXiv:​1207.​5127
go back to reference Tuluce Demiray, S., Bulut, H.: Some exact solutions of generalized Zakharov system. Waves Random Complex Media 25(1), 75–90 (2015)MathSciNetCrossRefADS Tuluce Demiray, S., Bulut, H.: Some exact solutions of generalized Zakharov system. Waves Random Complex Media 25(1), 75–90 (2015)MathSciNetCrossRefADS
go back to reference Yadav, R., Malik, S., Kumar, S., Sharma, R., Biswas, A., Yildirim, Y., Alghamdi, A.A.: Highly dispersive W-shaped and other optical solitons with quadratic-cubic nonlinearity: symmetry analysis and new Kudryashov’s method. Chaos Solitons Fractals 173, 113675 (2023)MathSciNetCrossRef Yadav, R., Malik, S., Kumar, S., Sharma, R., Biswas, A., Yildirim, Y., Alghamdi, A.A.: Highly dispersive W-shaped and other optical solitons with quadratic-cubic nonlinearity: symmetry analysis and new Kudryashov’s method. Chaos Solitons Fractals 173, 113675 (2023)MathSciNetCrossRef
go back to reference Younas, U., Ren, J.: Investigation of exact soliton solutions in magneto-optic waveguides and its stability analysis. Results Phys. 21, 103816 (2021)CrossRef Younas, U., Ren, J.: Investigation of exact soliton solutions in magneto-optic waveguides and its stability analysis. Results Phys. 21, 103816 (2021)CrossRef
go back to reference Younas, U., Bilal, M., Ren, J.: Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion. Opt. Quant. Electron. 53, 1–25 (2021)CrossRef Younas, U., Bilal, M., Ren, J.: Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion. Opt. Quant. Electron. 53, 1–25 (2021)CrossRef
go back to reference Younas, U., Bilal, M., Sulaiman, T.A., Ren, J., Yusuf, A.: On the exact soliton solutions and different wave structures to the double dispersive equation. Opt. Quant. Electron. 54, 1–22 (2022)CrossRef Younas, U., Bilal, M., Sulaiman, T.A., Ren, J., Yusuf, A.: On the exact soliton solutions and different wave structures to the double dispersive equation. Opt. Quant. Electron. 54, 1–22 (2022)CrossRef
go back to reference Younis, M., Seadawy, A.R., Bilal, M., Rehman, S.U., Latif, S., Rizvi, S.T.R.: Kinetics of phase separation in Fe-Cr-X (X= Mo, Cu) ternary alloys-a dynamical wave study. Int. J. Mod. Phys. B 35(21), 2150220 (2021)MathSciNetCrossRefADS Younis, M., Seadawy, A.R., Bilal, M., Rehman, S.U., Latif, S., Rizvi, S.T.R.: Kinetics of phase separation in Fe-Cr-X (X= Mo, Cu) ternary alloys-a dynamical wave study. Int. J. Mod. Phys. B 35(21), 2150220 (2021)MathSciNetCrossRefADS
go back to reference Zayed, E.M., Al-Nowehy, A.G.: The ϕ-model expansion method for solving the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity. Opt. Quant. Electron. 50(3), 1–19 (2018)CrossRef Zayed, E.M., Al-Nowehy, A.G.: The ϕ-model expansion method for solving the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity. Opt. Quant. Electron. 50(3), 1–19 (2018)CrossRef
go back to reference Zayed, E.M., Gepreel, K.A., Shohib, R.M., Alngar, M.E.: Solitons in magneto-optics waveguides for the nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index using the unified auxiliary equation method. Optik 235, 166602 (2021)CrossRefADS Zayed, E.M., Gepreel, K.A., Shohib, R.M., Alngar, M.E.: Solitons in magneto-optics waveguides for the nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index using the unified auxiliary equation method. Optik 235, 166602 (2021)CrossRefADS
go back to reference Zhou, Q., Liu, L., Zhang, H., Wei, C., Lu, J., Yu, H., Biswas, A.: Analytical study of Thirring optical solitons with parabolic law nonlinearity and spatio-temporal dispersion. Eur. Phys. J. Plus 130, 1–6 (2015)CrossRef Zhou, Q., Liu, L., Zhang, H., Wei, C., Lu, J., Yu, H., Biswas, A.: Analytical study of Thirring optical solitons with parabolic law nonlinearity and spatio-temporal dispersion. Eur. Phys. J. Plus 130, 1–6 (2015)CrossRef
Metadata
Title
Extraction of optical solitons for nonlinear Biswas–Milovic equation in magneto-optic waveguide
Authors
Tahir Shahzad
Muhammad Zafarullah Baber
Tukur Abdulkadir Sulaiman
Muhammad Ozair Ahmad
Nauman Ahmed
Publication date
01-01-2024
Publisher
Springer US
Published in
Optical and Quantum Electronics / Issue 1/2024
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-023-05531-z

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