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Erschienen in: Optical and Quantum Electronics 2/2023

01.02.2023

Optical solitons to the Perturbed Gerdjikov-Ivanov equation with quantic nonlinearity

verfasst von: Karmina K. Ali, Sibel Tarla, Tukur Abdulkadir Sulaiman, Resat Yilmazer

Erschienen in: Optical and Quantum Electronics | Ausgabe 2/2023

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Abstract

In this article, we examine the Perturbed Gerdjikov-Ivanov equation by using the Jacobi elliptic function expansion method. This results in obtaining distinct solutions including dark, bright, singular solitons, periodic waves, singular periodic waves, and Jacobi elliptic function solutions. The 2- and 3-dimensional graphs of the reported solutions are presented. The reported results may be useful in explaining the physical features of the studied equation.

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Literatur
Zurück zum Zitat Ablowitz, M.J., Ablowitz, M.A., Clarkson, P.A., Clarkson, P.A.: Solitons, nonlinear evolution equations and inverse scattering. Cambridge Univ Press., Cambridge (1991)CrossRefMATH Ablowitz, M.J., Ablowitz, M.A., Clarkson, P.A., Clarkson, P.A.: Solitons, nonlinear evolution equations and inverse scattering. Cambridge Univ Press., Cambridge (1991)CrossRefMATH
Zurück zum Zitat Ahmad, J.: Dynamics of Optical and Other Soliton Solutions in Fiber Bragg Gratings with Kerr Law and Stability Analysis. Arab. J. Sci. Eng. 30, 1–17 (2022) Ahmad, J.: Dynamics of Optical and Other Soliton Solutions in Fiber Bragg Gratings with Kerr Law and Stability Analysis. Arab. J. Sci. Eng. 30, 1–17 (2022)
Zurück zum Zitat Ali, K.K., Varol, A.: Weissenberg and Williamson MHD flow over a stretching surface with thermal radiation and chemical reaction. JP J. Heat Mass Transf. 18(1), 15 (2019)CrossRef Ali, K.K., Varol, A.: Weissenberg and Williamson MHD flow over a stretching surface with thermal radiation and chemical reaction. JP J. Heat Mass Transf. 18(1), 15 (2019)CrossRef
Zurück zum Zitat Ali, M., Walboomers, X.F.J., Jansen, A., Yang, F.: Influence of formulation parameters on encapsulation of doxycycline in PLGA microspheres prepared by double emulsion technique for the treatment of periodontitis. J. Drug Deliv. Sci. Technol. 52, 263–271 (2019)CrossRef Ali, M., Walboomers, X.F.J., Jansen, A., Yang, F.: Influence of formulation parameters on encapsulation of doxycycline in PLGA microspheres prepared by double emulsion technique for the treatment of periodontitis. J. Drug Deliv. Sci. Technol. 52, 263–271 (2019)CrossRef
Zurück zum Zitat Ali, K.K., Yilmazer, R., Bulut, H., Aktürk, T., Osman, M.S.: Abundant exact solutions to the strain wave equation in micro-structured solids. Mod. Phys. Lett. B. 35(26), 1–15 (2021)MathSciNetCrossRef Ali, K.K., Yilmazer, R., Bulut, H., Aktürk, T., Osman, M.S.: Abundant exact solutions to the strain wave equation in micro-structured solids. Mod. Phys. Lett. B. 35(26), 1–15 (2021)MathSciNetCrossRef
Zurück zum Zitat Ali, K.K., Yokus, A., Seadawy, A.R., Yilmazer, R.: The ion sound and Langmuir waves dynamical system via computational modified generalized exponential rational function. Chaos Solitons Fractals 161, 112381 (2022)MathSciNetCrossRefMATH Ali, K.K., Yokus, A., Seadawy, A.R., Yilmazer, R.: The ion sound and Langmuir waves dynamical system via computational modified generalized exponential rational function. Chaos Solitons Fractals 161, 112381 (2022)MathSciNetCrossRefMATH
Zurück zum Zitat Alshehri, A.M., Alshehri, H.M., Alshreef, A.N., Kara, A.H., Biswas, A., Yıldırım, Y.: Conservation laws for dispersive optical solitons with Radhakrishnan-Kundu-Lakshmanan model having quadrupled power-law of self-phase modulation. Optik. 267, 169715 (2022)ADSCrossRef Alshehri, A.M., Alshehri, H.M., Alshreef, A.N., Kara, A.H., Biswas, A., Yıldırım, Y.: Conservation laws for dispersive optical solitons with Radhakrishnan-Kundu-Lakshmanan model having quadrupled power-law of self-phase modulation. Optik. 267, 169715 (2022)ADSCrossRef
Zurück zum Zitat Alshehri, H.M., Maturi, D.A., Al-Bogami, D.H., Biswas, A.: Sequel to Quasi-monochromatic dynamical system of cubic-quartic optical solitons with Kerr law of nonlinear refractive index’’ (Power law). Optik. 267, 169623 (2022)ADSCrossRef Alshehri, H.M., Maturi, D.A., Al-Bogami, D.H., Biswas, A.: Sequel to Quasi-monochromatic dynamical system of cubic-quartic optical solitons with Kerr law of nonlinear refractive index’’ (Power law). Optik. 267, 169623 (2022)ADSCrossRef
Zurück zum Zitat Alshehri, H.M., Maturi, D.A., Al-Bogami, D.H., Yıldırım, Y., Biswas, A.: Quasi-monochromatic dynamical system of cubic-quartic optical solitons with Kerr law of nonlinear refractive index. Optik. 267, 169622 (2022)ADSCrossRef Alshehri, H.M., Maturi, D.A., Al-Bogami, D.H., Yıldırım, Y., Biswas, A.: Quasi-monochromatic dynamical system of cubic-quartic optical solitons with Kerr law of nonlinear refractive index. Optik. 267, 169622 (2022)ADSCrossRef
Zurück zum Zitat Altwaty, A.A.: Numerous new Jacobi elliptic function solutions for fractional space-time perturbed Gerdjikov-Ivanov equation with conformable derivative. Int. J. Nonlinear Anal. Appl. 13(2), 1009–1021 (2022) Altwaty, A.A.: Numerous new Jacobi elliptic function solutions for fractional space-time perturbed Gerdjikov-Ivanov equation with conformable derivative. Int. J. Nonlinear Anal. Appl. 13(2), 1009–1021 (2022)
Zurück zum Zitat Biswas, A., Ekici, M., Sonmezoglu, A., Zhou, Q., Moshokoa, S.P., Belic, M.: Chirped solitons in optical metamaterials with parabolic law nonlinearity by extended trial function method. Optik. 160, 92–99 (2018)ADSCrossRef Biswas, A., Ekici, M., Sonmezoglu, A., Zhou, Q., Moshokoa, S.P., Belic, M.: Chirped solitons in optical metamaterials with parabolic law nonlinearity by extended trial function method. Optik. 160, 92–99 (2018)ADSCrossRef
Zurück zum Zitat Campbell, D.K.: Nonlinear physics: Fresh breather. Nature. 432(7016), 455–456 (2004)ADSCrossRef Campbell, D.K.: Nonlinear physics: Fresh breather. Nature. 432(7016), 455–456 (2004)ADSCrossRef
Zurück zum Zitat Hosseini, K., Mirzazadeh, M., Ilie, M., Radmehr, S.: Dynamics of optical solitons in the perturbed Gerdjikov-Ivanov equation. Optik. 206, 164350 (2020)ADSCrossRef Hosseini, K., Mirzazadeh, M., Ilie, M., Radmehr, S.: Dynamics of optical solitons in the perturbed Gerdjikov-Ivanov equation. Optik. 206, 164350 (2020)ADSCrossRef
Zurück zum Zitat Hubert, M.B., Justin, M., Betchewe, G., Doka, S.Y., Biswas, A., Zhou, Q., Ekici, M., Moshokoa, S.P., Belic, M.: Optical solitons with modified extended direct algebraic method for quadratic-cubic nonlinearity. Optik. 162, 161–171 (2018)ADSCrossRef Hubert, M.B., Justin, M., Betchewe, G., Doka, S.Y., Biswas, A., Zhou, Q., Ekici, M., Moshokoa, S.P., Belic, M.: Optical solitons with modified extended direct algebraic method for quadratic-cubic nonlinearity. Optik. 162, 161–171 (2018)ADSCrossRef
Zurück zum Zitat Ismael, H.F., Bulut, H., Osman, M.S.: The N-soliton, fusion, rational and breather solutions of two extensions of the (2+ 1)-dimensional Bogoyavlenskii-Schieff equation. Nonlinear Dyn. 107(4), 3791–3803 (2022)CrossRef Ismael, H.F., Bulut, H., Osman, M.S.: The N-soliton, fusion, rational and breather solutions of two extensions of the (2+ 1)-dimensional Bogoyavlenskii-Schieff equation. Nonlinear Dyn. 107(4), 3791–3803 (2022)CrossRef
Zurück zum Zitat Ismael, H.F., Murad, M.A.S., Bulut, H.: Various exact wave solutions for KdV equation with time-variable coefficients. J. Ocean Eng. Sci. 7(5), 409–418 (2021)CrossRef Ismael, H.F., Murad, M.A.S., Bulut, H.: Various exact wave solutions for KdV equation with time-variable coefficients. J. Ocean Eng. Sci. 7(5), 409–418 (2021)CrossRef
Zurück zum Zitat Ismael, H.F., Murad, M.A.S., Bulut, H.: M-lump waves and their interaction with multi-soliton solutions for a generalized Kadomtsev-Petviashvili equation in (3+ 1)-dimensions. Chinese J. Physics 77, 1357–1364 (2022)ADSMathSciNetCrossRef Ismael, H.F., Murad, M.A.S., Bulut, H.: M-lump waves and their interaction with multi-soliton solutions for a generalized Kadomtsev-Petviashvili equation in (3+ 1)-dimensions. Chinese J. Physics 77, 1357–1364 (2022)ADSMathSciNetCrossRef
Zurück zum Zitat Khalili Golmankhaneh, A., Ali, K.K., Yilmazer, R., Kaabar, M.: Economic models involving time fractal. J. Math. Model. Financ. 1(1), 159–178 (2021) Khalili Golmankhaneh, A., Ali, K.K., Yilmazer, R., Kaabar, M.: Economic models involving time fractal. J. Math. Model. Financ. 1(1), 159–178 (2021)
Zurück zum Zitat Korenberg, M.J., Hunter, I.W.: The identification of nonlinear biological systems: Volterra kernel approaches. Ann. Biomed. Eng. 24(2), 250–268 (1996)CrossRef Korenberg, M.J., Hunter, I.W.: The identification of nonlinear biological systems: Volterra kernel approaches. Ann. Biomed. Eng. 24(2), 250–268 (1996)CrossRef
Zurück zum Zitat Manafian, J., Ilhan, O.A., Ismael, H.F., Mohammed, S.A., Mazanova, S.: Periodic wave solutions and stability analysis for the (3+ 1)-D potential-YTSF equation arising in fluid mechanics. Int. J. Comput. Math. 98(8), 1594–1616 (2021)MathSciNetCrossRefMATH Manafian, J., Ilhan, O.A., Ismael, H.F., Mohammed, S.A., Mazanova, S.: Periodic wave solutions and stability analysis for the (3+ 1)-D potential-YTSF equation arising in fluid mechanics. Int. J. Comput. Math. 98(8), 1594–1616 (2021)MathSciNetCrossRefMATH
Zurück zum Zitat Mosconi, F., Julou, T., Desprat, N., Sinha, D.K., Allemand, J.F., Vincent, C., Bensimon, D.: Some nonlinear challenges in biology. Nonlinearity. 21(8), T131 (2008)ADSMathSciNetCrossRefMATH Mosconi, F., Julou, T., Desprat, N., Sinha, D.K., Allemand, J.F., Vincent, C., Bensimon, D.: Some nonlinear challenges in biology. Nonlinearity. 21(8), T131 (2008)ADSMathSciNetCrossRefMATH
Zurück zum Zitat Muniyappan, A., Monisha, P., Nivetha, V.: Generation of wing-shaped dark soliton for perturbed Gerdjikov-Ivanov equation in optical fibre. Optik. 230, 166328 (2021)CrossRef Muniyappan, A., Monisha, P., Nivetha, V.: Generation of wing-shaped dark soliton for perturbed Gerdjikov-Ivanov equation in optical fibre. Optik. 230, 166328 (2021)CrossRef
Zurück zum Zitat Rehman, S.U., Bilal, M., Ahmad, J.: The study of solitary wave solutions to the time conformable Schrödinger system by a powerful computational technique. Opt. Quantum Electron. 54(4), 1–18 (2022)CrossRef Rehman, S.U., Bilal, M., Ahmad, J.: The study of solitary wave solutions to the time conformable Schrödinger system by a powerful computational technique. Opt. Quantum Electron. 54(4), 1–18 (2022)CrossRef
Zurück zum Zitat Rehman, S.U., Bilal, M., Inc, M., Younas, U., Rezazadeh, H., Younis, M., Mirhosseini-Alizamini, S.M.: Investigation of pure-cubic optical solitons in nonlinear optics. Opt. Quantum Electron. 54(7), 1–21 (2022)CrossRef Rehman, S.U., Bilal, M., Inc, M., Younas, U., Rezazadeh, H., Younis, M., Mirhosseini-Alizamini, S.M.: Investigation of pure-cubic optical solitons in nonlinear optics. Opt. Quantum Electron. 54(7), 1–21 (2022)CrossRef
Zurück zum Zitat Rehman, S.U., Seadawy, A.R., Younis, M., Rizvi, S.T.R.: On study of modulation instability and optical soliton solutions: the chiral nonlinear Schrödinger dynamical equation. Opt. Quantum Electron. 53(8), 1–17 (2021)CrossRef Rehman, S.U., Seadawy, A.R., Younis, M., Rizvi, S.T.R.: On study of modulation instability and optical soliton solutions: the chiral nonlinear Schrödinger dynamical equation. Opt. Quantum Electron. 53(8), 1–17 (2021)CrossRef
Zurück zum Zitat Samir, I., Badra, N., Seadawy, A.R., Ahmed, H.M., Arnous, A.H.: Computational extracting solutions for the perturbed Gerdjikov-Ivanov equation by using an improved modified extended analytical approach. J. Geom. Physics. 176, 104514 (2022)MathSciNetCrossRefMATH Samir, I., Badra, N., Seadawy, A.R., Ahmed, H.M., Arnous, A.H.: Computational extracting solutions for the perturbed Gerdjikov-Ivanov equation by using an improved modified extended analytical approach. J. Geom. Physics. 176, 104514 (2022)MathSciNetCrossRefMATH
Zurück zum Zitat Tarla, S., Ali, K.K., Yilmazer, R.: Newly modified unified auxiliary equation method and its applications. Optik. 269, 169880 (2022)ADSCrossRef Tarla, S., Ali, K.K., Yilmazer, R.: Newly modified unified auxiliary equation method and its applications. Optik. 269, 169880 (2022)ADSCrossRef
Zurück zum Zitat Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: The dynamic behaviors of the Radhakrishnan-Kundu-Lakshmanan equation by Jacobi elliptic function expansion technique. Opt. Quantum Electron. 54(5), 1–12 (2022)CrossRef Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: The dynamic behaviors of the Radhakrishnan-Kundu-Lakshmanan equation by Jacobi elliptic function expansion technique. Opt. Quantum Electron. 54(5), 1–12 (2022)CrossRef
Zurück zum Zitat Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method. Opt. Quantum Electron. 54(2), 1–12 (2022)CrossRef Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method. Opt. Quantum Electron. 54(2), 1–12 (2022)CrossRef
Zurück zum Zitat Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: Propagation of solitons for the Hamiltonian amplitude equation via an analytical technique. Mod. Phys. Lett. B. 36(23), 2250120 (2022)ADSCrossRef Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: Propagation of solitons for the Hamiltonian amplitude equation via an analytical technique. Mod. Phys. Lett. B. 36(23), 2250120 (2022)ADSCrossRef
Zurück zum Zitat Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: On dynamical behavior for optical solitons sustained by the perturbed Chen-Lee-Liu model. Commun. Theor. Phys. 74(7), 075005 (2022)ADSMathSciNetCrossRef Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: On dynamical behavior for optical solitons sustained by the perturbed Chen-Lee-Liu model. Commun. Theor. Phys. 74(7), 075005 (2022)ADSMathSciNetCrossRef
Zurück zum Zitat Ur-Rehman, S., Ahmad, J.: Dynamics of optical and multiple lump solutions to the fractional coupled nonlinear Schrödinger equation. Opt. Quantum Electron. 54(10), 1–26 (2022)CrossRef Ur-Rehman, S., Ahmad, J.: Dynamics of optical and multiple lump solutions to the fractional coupled nonlinear Schrödinger equation. Opt. Quantum Electron. 54(10), 1–26 (2022)CrossRef
Zurück zum Zitat Younis, M., Bilal, M., Rehman, S.U., Seadawy, A.R., Rizvi, S.T.R.: Perturbed optical solitons with conformable time-space fractional Gerdjikov-Ivanov equation. Math. Sci. 35, 1–13 (2021) Younis, M., Bilal, M., Rehman, S.U., Seadawy, A.R., Rizvi, S.T.R.: Perturbed optical solitons with conformable time-space fractional Gerdjikov-Ivanov equation. Math. Sci. 35, 1–13 (2021)
Metadaten
Titel
Optical solitons to the Perturbed Gerdjikov-Ivanov equation with quantic nonlinearity
verfasst von
Karmina K. Ali
Sibel Tarla
Tukur Abdulkadir Sulaiman
Resat Yilmazer
Publikationsdatum
01.02.2023
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 2/2023
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-022-04418-9

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