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Erschienen in: Optical and Quantum Electronics 5/2022

01.05.2022

The dynamic behaviors of the Radhakrishnan–Kundu–Lakshmanan equation by Jacobi elliptic function expansion technique

verfasst von: Sibel Tarla, Karmina K. Ali, Resat Yilmazer, M. S. Osman

Erschienen in: Optical and Quantum Electronics | Ausgabe 5/2022

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Abstract

In this study, we express the Radhakrishnan–Kundu–Lakshmanan equation with an arbitrary index of \(n\in Q\). We investigated the solitary wave solutions of the Radhakrishnan–Kundu–Lakshmanan equation by mean of the Jacobi elliptic function expansion technique. As a result, we constructed several distinct solutions include dark, bright, singular, periodic, hyperbolic, trigonometric, and Jacobi elliptic function types solutions. To highlight the dynamic behavior of the generated solutions, specific values for the parameters are also assigned. The above techniques could also be employed to get a variety of exact solutions for other nonlinear models in physics, applied mathematics, and engineering.

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Literatur
Zurück zum Zitat Abdel-Gawad, H.I., Osman, M.: Exact solutions of the Korteweg-de Vries equation with space and time dependent coefficients by the extended unified method. Indian J. Pure Appl. Math. 45(1), 1–12 (2014)MathSciNetMATHCrossRef Abdel-Gawad, H.I., Osman, M.: Exact solutions of the Korteweg-de Vries equation with space and time dependent coefficients by the extended unified method. Indian J. Pure Appl. Math. 45(1), 1–12 (2014)MathSciNetMATHCrossRef
Zurück zum Zitat Ahmed, H.M., Rabie, W.B., Ragusa, M.A.: Optical solitons and other solutions to Kaup–Newell equation with Jacobi elliptic function expansion method. Anal. Math. Phys. 11(1), 23 (2021)MathSciNetMATHCrossRef Ahmed, H.M., Rabie, W.B., Ragusa, M.A.: Optical solitons and other solutions to Kaup–Newell equation with Jacobi elliptic function expansion method. Anal. Math. Phys. 11(1), 23 (2021)MathSciNetMATHCrossRef
Zurück zum Zitat Ali, A.T.: New generalized Jacobi elliptic function rational expansion method. J. Comput. Appl. Math. 235, 4117–4127 (2011)MathSciNetMATHCrossRef Ali, A.T.: New generalized Jacobi elliptic function rational expansion method. J. Comput. Appl. Math. 235, 4117–4127 (2011)MathSciNetMATHCrossRef
Zurück zum Zitat Ali, K.K., Osman, M.S., Baskonus, H.M., Elazabb, N.S., Ilhan, E.: Analytical and numerical study of the HIV-1 infection of CD4+ T-cells conformable fractional mathematical model that causes acquired immunodeficiency syndrome with the effect of antiviral drug therapy. Math. Methods Appl. Sci. (2020a). https://doi.org/10.1002/mma.7022CrossRef Ali, K.K., Osman, M.S., Baskonus, H.M., Elazabb, N.S., Ilhan, E.: Analytical and numerical study of the HIV-1 infection of CD4+ T-cells conformable fractional mathematical model that causes acquired immunodeficiency syndrome with the effect of antiviral drug therapy. Math. Methods Appl. Sci. (2020a). https://​doi.​org/​10.​1002/​mma.​7022CrossRef
Zurück zum Zitat Ali, K.K., Yılmazer, R., Baskonus, H.M., Bulut, H.: Modulation instability analysis and analytical solutions to the system of equations for the ion sound and Langmuir waves. Phys. Scr. 95(6), 065602 (2020b)ADSCrossRef Ali, K.K., Yılmazer, R., Baskonus, H.M., Bulut, H.: Modulation instability analysis and analytical solutions to the system of equations for the ion sound and Langmuir waves. Phys. Scr. 95(6), 065602 (2020b)ADSCrossRef
Zurück zum Zitat Ali, K.K., Seadawy, A.R., Yokus, A., Yılmazer, R., Bulut, H.: Propagation of dispersive wave solutions for (3+ 1)-dimensional nonlinear modified Zakharov–Kuznetsov equation in plasma physics. Int. J. Mod. Phys. B 34(25), 2050227 (2020c)ADSMathSciNetMATHCrossRef Ali, K.K., Seadawy, A.R., Yokus, A., Yılmazer, R., Bulut, H.: Propagation of dispersive wave solutions for (3+ 1)-dimensional nonlinear modified Zakharov–Kuznetsov equation in plasma physics. Int. J. Mod. Phys. B 34(25), 2050227 (2020c)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Ali, K.K., Yılmazer, R., Yokus, A., Bulut, H.: Analytical solutions for the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation in plasma physics. Physica A 548, 124327 (2020d)MathSciNetMATHCrossRef Ali, K.K., Yılmazer, R., Yokus, A., Bulut, H.: Analytical solutions for the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation in plasma physics. Physica A 548, 124327 (2020d)MathSciNetMATHCrossRef
Zurück zum Zitat Ali, K.K., Yılmazer, R., Yokus, A., Bulut, H.: Analytical solutions for the (3+ 1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation in plasma physics. Physica A 548, 124327 (2020e)MathSciNetMATHCrossRef Ali, K.K., Yılmazer, R., Yokus, A., Bulut, H.: Analytical solutions for the (3+ 1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation in plasma physics. Physica A 548, 124327 (2020e)MathSciNetMATHCrossRef
Zurück zum Zitat Ali, K.K., Yılmazer, 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), 2150439 (2021)ADSMathSciNetCrossRef Ali, K.K., Yılmazer, 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), 2150439 (2021)ADSMathSciNetCrossRef
Zurück zum Zitat Ali, K.K., Yılmazer, R., Osman, M.S.: Dynamic behavior of the (3+ 1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation. Opt. Quant. Electron. 54(3), 160 (2022)CrossRef Ali, K.K., Yılmazer, R., Osman, M.S.: Dynamic behavior of the (3+ 1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation. Opt. Quant. Electron. 54(3), 160 (2022)CrossRef
Zurück zum Zitat Alquran, M., Jarrah, A.: Jacobi elliptic function solutions for a two-mode KdV equation. J. King Saud Univ. Sci. 31, 485–489 (2019)CrossRef Alquran, M., Jarrah, A.: Jacobi elliptic function solutions for a two-mode KdV equation. J. King Saud Univ. Sci. 31, 485–489 (2019)CrossRef
Zurück zum Zitat Arshad, M., Lu, D., Rehman, M.U., Ahmed, I., Sultan, A.M.: Optical solitary wave and elliptic function solutions of the Fokas–Lenells equation in the presence of perturbation terms and its modulation instability. Phys. Scr. 94, 105202 (2019)ADSCrossRef Arshad, M., Lu, D., Rehman, M.U., Ahmed, I., Sultan, A.M.: Optical solitary wave and elliptic function solutions of the Fokas–Lenells equation in the presence of perturbation terms and its modulation instability. Phys. Scr. 94, 105202 (2019)ADSCrossRef
Zurück zum Zitat Arshed, S., Biswas, A., Guggilla, P., Alshomrani, A.S.: Optical solitons for Radhakrishnan-Kundu-Lakshmanan equation with full nonlinearity. Phys. Lett. A 384(26), 126191 (2020)MathSciNetMATHCrossRef Arshed, S., Biswas, A., Guggilla, P., Alshomrani, A.S.: Optical solitons for Radhakrishnan-Kundu-Lakshmanan equation with full nonlinearity. Phys. Lett. A 384(26), 126191 (2020)MathSciNetMATHCrossRef
Zurück zum Zitat Bhrawy, A.H., Tharwat, M.M., Yıldirim, A., Abdelkawy, M.A.: A Jacobi elliptic function method for nonlinear arrays of vortices. Indian J. Phys. 86(12), 1107–1113 (2012)ADSCrossRef Bhrawy, A.H., Tharwat, M.M., Yıldirim, A., Abdelkawy, M.A.: A Jacobi elliptic function method for nonlinear arrays of vortices. Indian J. Phys. 86(12), 1107–1113 (2012)ADSCrossRef
Zurück zum Zitat Biswas, A.: Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by traveling wave hypothesis. Optik 171, 217–220 (2018)ADSCrossRef Biswas, A.: Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by traveling wave hypothesis. Optik 171, 217–220 (2018)ADSCrossRef
Zurück zum Zitat Biswas, A., Ekici, M., Sonmezoglu, A., Alshomrani, A.S.: Optical solitons with Radhakrishnan–Kundu–Lakshmanan equation by extended trial function scheme. Optik 160, 415–427 (2018)ADSCrossRef Biswas, A., Ekici, M., Sonmezoglu, A., Alshomrani, A.S.: Optical solitons with Radhakrishnan–Kundu–Lakshmanan equation by extended trial function scheme. Optik 160, 415–427 (2018)ADSCrossRef
Zurück zum Zitat El-Sheikh, M.M.A., Ahmed, H.M., Arnous, A.H., Rabie, W.B.: Optical solitons and other solutions in birefringent fibers with Biswas–Arshed equation by Jacobi’s elliptic function approach. Optik 202, 163546 (2020) El-Sheikh, M.M.A., Ahmed, H.M., Arnous, A.H., Rabie, W.B.: Optical solitons and other solutions in birefringent fibers with Biswas–Arshed equation by Jacobi’s elliptic function approach. Optik 202, 163546 (2020)
Zurück zum Zitat Feng, Q., Meng, F.: Traveling wave solutions for fractional partial differential equations arising in mathematical physics by an improved fractional Jacobi elliptic equation method. Math. Methods Appl. Sci. 40, 3676–3686 (2017)ADSMathSciNetMATHCrossRef Feng, Q., Meng, F.: Traveling wave solutions for fractional partial differential equations arising in mathematical physics by an improved fractional Jacobi elliptic equation method. Math. Methods Appl. Sci. 40, 3676–3686 (2017)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Fu, Z., Liu, S., Liu, S., Zhao, Q.: New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Phys. Lett. A 290, 72–76 (2001)ADSMathSciNetMATHCrossRef Fu, Z., Liu, S., Liu, S., Zhao, Q.: New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Phys. Lett. A 290, 72–76 (2001)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Garai, S., Ghose-Choudhury, A.: On the solution of the generalized Radhakrishnan–Kundu–Lakshmanan equation. Optik 243, 167374 (2021)ADSCrossRef Garai, S., Ghose-Choudhury, A.: On the solution of the generalized Radhakrishnan–Kundu–Lakshmanan equation. Optik 243, 167374 (2021)ADSCrossRef
Zurück zum Zitat Ghanbari, B., Gómez-Aguilar, J.F.: Optical soliton solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation. Mod. Phys. Lett. B 33(32), 1950402 (2019)ADSMathSciNetCrossRef Ghanbari, B., Gómez-Aguilar, J.F.: Optical soliton solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation. Mod. Phys. Lett. B 33(32), 1950402 (2019)ADSMathSciNetCrossRef
Zurück zum Zitat Ghanbari, B., Kumar, S., Niwas, M., Baleanu, D.: The Lie symmetry analysis and exact Jacobi elliptic solutions for the Kawahara–KdV type equations. Results Phys. 23, 104006 (2021)CrossRef Ghanbari, B., Kumar, S., Niwas, M., Baleanu, D.: The Lie symmetry analysis and exact Jacobi elliptic solutions for the Kawahara–KdV type equations. Results Phys. 23, 104006 (2021)CrossRef
Zurück zum Zitat Hosseini, K., Matinfar, M., Mirzazadeh, M.: A (3+1)-dimensional resonant nonlinear Schrödinger equation and its Jacobi elliptic and exponential function solutions. Optik 207, 164458 (2020)ADSCrossRef Hosseini, K., Matinfar, M., Mirzazadeh, M.: A (3+1)-dimensional resonant nonlinear Schrödinger equation and its Jacobi elliptic and exponential function solutions. Optik 207, 164458 (2020)ADSCrossRef
Zurück zum Zitat Inc, M., Ergüt, M.: Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method. Appl. Math. E-Notes 5, 89–96 (2005)MathSciNetMATH Inc, M., Ergüt, M.: Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method. Appl. Math. E-Notes 5, 89–96 (2005)MathSciNetMATH
Zurück zum Zitat Ismael, H.F., Bulut, H.: Nonlinear dynamics of (2+ 1)-dimensional Bogoyavlenskii–Schieff equation arising in plasma physics. Math. Methods Appl. Sci. 44(13), 10321–10330 (2021a)ADSMathSciNetMATHCrossRef Ismael, H.F., Bulut, H.: Nonlinear dynamics of (2+ 1)-dimensional Bogoyavlenskii–Schieff equation arising in plasma physics. Math. Methods Appl. Sci. 44(13), 10321–10330 (2021a)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Ismael, H.F., Bulut, H.: Nonlinear dynamics of (2 + 1)-dimensional Bogoyavlenskii–Schieff equation arising in plasma physics. Math. Methods Appl. Sci. 44(13), 10321–10330 (2021b)ADSMathSciNetMATHCrossRef Ismael, H.F., Bulut, H.: Nonlinear dynamics of (2 + 1)-dimensional Bogoyavlenskii–Schieff equation arising in plasma physics. Math. Methods Appl. Sci. 44(13), 10321–10330 (2021b)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Ismael, H.F., Bulut, H., Baskonus, H.M.: Optical soliton solutions to the Fokas–Lenells equation via sine-Gordon expansion method and $(m+G^{\prime } G)$-expansion method. Pramana 94(1), 35 (2020)ADSCrossRef Ismael, H.F., Bulut, H., Baskonus, H.M.: Optical soliton solutions to the Fokas–Lenells equation via sine-Gordon expansion method and $(m+G^{\prime } G)$-expansion method. Pramana 94(1), 35 (2020)ADSCrossRef
Zurück zum Zitat Ismael, H.F., Seadaway, A., Bulut, H.: Rational solutions and the interaction solutions to the (2 + 1)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation. Int. J. Comput. Math. 98(12), 2369–2377 (2021b)MathSciNetMATHCrossRef Ismael, H.F., Seadaway, A., Bulut, H.: Rational solutions and the interaction solutions to the (2 + 1)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation. Int. J. Comput. Math. 98(12), 2369–2377 (2021b)MathSciNetMATHCrossRef
Zurück zum Zitat Ismael, H.F., Atas, S.S., Bulut, H., Osman, M.S.: Analytical solutions to the M-derivative resonant Davey–Stewartson equations. Mod. Phys. Lett. B 35(30), 2150455 (2021c)ADSMathSciNetCrossRef Ismael, H.F., Atas, S.S., Bulut, H., Osman, M.S.: Analytical solutions to the M-derivative resonant Davey–Stewartson equations. Mod. Phys. Lett. B 35(30), 2150455 (2021c)ADSMathSciNetCrossRef
Zurück zum Zitat Khalid, A., Rehan, A., Nisar, K.S., Osman, M.S.: Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit. Phys. Scr. 96(10), 104001 (2021)ADSCrossRef Khalid, A., Rehan, A., Nisar, K.S., Osman, M.S.: Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit. Phys. Scr. 96(10), 104001 (2021)ADSCrossRef
Zurück zum Zitat Kudryashov, N.A.: General solution of the traveling wave reduction for the perturbed Chen–Lee–Liu equation. Optik 186, 339–349 (2019)ADSCrossRef Kudryashov, N.A.: General solution of the traveling wave reduction for the perturbed Chen–Lee–Liu equation. Optik 186, 339–349 (2019)ADSCrossRef
Zurück zum Zitat Kudryashov, N.A.: The Radhakrishnan–Kundu–Lakshmanan equation with arbitrary refractive index and its exact solutions. Optik 238, 166738 (2021)ADSCrossRef Kudryashov, N.A.: The Radhakrishnan–Kundu–Lakshmanan equation with arbitrary refractive index and its exact solutions. Optik 238, 166738 (2021)ADSCrossRef
Zurück zum Zitat Kumar, V.S., Rezazadeh, H., Eslami, M., Izadi, F., Osman, M.S.: Jacobi elliptic function expansion method for solving KdV equation with conformable derivative and dual-power law nonlinearity. Int. J. Appl. Comput. Math. 5(5), 127 (2019)MathSciNetMATHCrossRef Kumar, V.S., Rezazadeh, H., Eslami, M., Izadi, F., Osman, M.S.: Jacobi elliptic function expansion method for solving KdV equation with conformable derivative and dual-power law nonlinearity. Int. J. Appl. Comput. Math. 5(5), 127 (2019)MathSciNetMATHCrossRef
Zurück zum Zitat Kumar, S., Niwas, M., Osman, M.S., Abdou, M.: Abundant different types of exact-soliton solutions to the (4+ 1)-dimensional Fokas and (2+ 1)-dimensional Breaking soliton equations. Commun. Theor. Phys. 73(10), 105007 (2021)ADSMathSciNetCrossRef Kumar, S., Niwas, M., Osman, M.S., Abdou, M.: Abundant different types of exact-soliton solutions to the (4+ 1)-dimensional Fokas and (2+ 1)-dimensional Breaking soliton equations. Commun. Theor. Phys. 73(10), 105007 (2021)ADSMathSciNetCrossRef
Zurück zum Zitat Li, Y., Celik, E., Guirao, J.L.G., Saeed, T., Baskonus, H.M.: On the modulation instability analysis and deeper properties of the cubic nonlinear Schrödinger’s equation with repulsive $\delta $-potential. Results Phys. 25, 104303 (2021) Li, Y., Celik, E., Guirao, J.L.G., Saeed, T., Baskonus, H.M.: On the modulation instability analysis and deeper properties of the cubic nonlinear Schrödinger’s equation with repulsive $\delta $-potential. Results Phys. 25, 104303 (2021)
Zurück zum Zitat Liu, J.G., Zhu, W.H., Osman, M.S., Ma, W.X.: An explicit plethora of different classes of interactive lump solutions for an extension form of 3D-Jimbo-Miwa model. Eur. Phys. J. Plus 135(5), 412 (2020)CrossRef Liu, J.G., Zhu, W.H., Osman, M.S., Ma, W.X.: An explicit plethora of different classes of interactive lump solutions for an extension form of 3D-Jimbo-Miwa model. Eur. Phys. J. Plus 135(5), 412 (2020)CrossRef
Zurück zum Zitat Liu, D., Ju, X., Ilhan, O.A., Manafian, J., Ismael, H.F.: Multi-waves, breathers, periodic and cross-kink solutions to the (2+ 1)-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation. J. Ocean Univ. China 20(1), 35–44 (2021)ADSCrossRef Liu, D., Ju, X., Ilhan, O.A., Manafian, J., Ismael, H.F.: Multi-waves, breathers, periodic and cross-kink solutions to the (2+ 1)-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation. J. Ocean Univ. China 20(1), 35–44 (2021)ADSCrossRef
Zurück zum Zitat Ma, H.C., Zhang, Z.P., Deng, A.P.: A new periodic solution to Jacobi elliptic functions of MKdV equation and BBM equation. Acta Math. Appl. Sin. 28, 409–415 (2012)MathSciNetMATHCrossRef Ma, H.C., Zhang, Z.P., Deng, A.P.: A new periodic solution to Jacobi elliptic functions of MKdV equation and BBM equation. Acta Math. Appl. Sin. 28, 409–415 (2012)MathSciNetMATHCrossRef
Zurück zum Zitat Manafian, J., Ilhan, O.A., Ali, K.K., Abid, S.: Cross-kink wave solutions and semi-inverse variational method for (3+1)-dimensional potential-YTSF equation. East Asian J. Appl. Math. 10(3), 549–565 (2020)MathSciNetMATHCrossRef Manafian, J., Ilhan, O.A., Ali, K.K., Abid, S.: Cross-kink wave solutions and semi-inverse variational method for (3+1)-dimensional potential-YTSF equation. East Asian J. Appl. Math. 10(3), 549–565 (2020)MathSciNetMATHCrossRef
Zurück zum Zitat Mvogo, A., Mouassom, L.F., Nyam, F.E.A., Mbane, C.B.: Exact solitary waves for the 2D Sasa-Satsuma equation. Chaos Solitons Fractals 133, 109657 (2020)MathSciNetMATHCrossRef Mvogo, A., Mouassom, L.F., Nyam, F.E.A., Mbane, C.B.: Exact solitary waves for the 2D Sasa-Satsuma equation. Chaos Solitons Fractals 133, 109657 (2020)MathSciNetMATHCrossRef
Zurück zum Zitat Osman, M.S., Machado, J.A.T., Baleanu, D.: On nonautonomous complex wave solutions described by the coupled Schrödinger–Boussinesq equation with variable-coefficients. Opt. Quant. Electron. 50(2), 73 (2018)CrossRef Osman, M.S., Machado, J.A.T., Baleanu, D.: On nonautonomous complex wave solutions described by the coupled Schrödinger–Boussinesq equation with variable-coefficients. Opt. Quant. Electron. 50(2), 73 (2018)CrossRef
Zurück zum Zitat Ozdemir, N., Esen, H., Secer, A., Bayram, M., Sulaiman, T.A., Yusuf, A., Aydin, H.: Optical solitons and other solutions to the Radhakrishnan–Kundu–Lakshmanan equation. Optik 242, 167363 (2021)ADSCrossRef Ozdemir, N., Esen, H., Secer, A., Bayram, M., Sulaiman, T.A., Yusuf, A., Aydin, H.: Optical solitons and other solutions to the Radhakrishnan–Kundu–Lakshmanan equation. Optik 242, 167363 (2021)ADSCrossRef
Zurück zum Zitat Rizvi, S.T.R., Seadawy, A.R., Younis, M., Ahmad, S., Ali, K.: Weierstrass and Jacobi elliptic solutions with some new dromions to Maccari system. Int. J. Mod. Phys. B 35(25), 2150257 (2021)ADSMATHCrossRef Rizvi, S.T.R., Seadawy, A.R., Younis, M., Ahmad, S., Ali, K.: Weierstrass and Jacobi elliptic solutions with some new dromions to Maccari system. Int. J. Mod. Phys. B 35(25), 2150257 (2021)ADSMATHCrossRef
Zurück zum Zitat Sabi’u, J., Tala-Tebue, E., Rezazadeh, H., Arshed, S., Bekir, A.: Optical solitons for the decoupled nonlinear Schrödinger equation using Jacobi elliptic approach. Commun. Theor. Phys. 73(7), 075003 (2021) Sabi’u, J., Tala-Tebue, E., Rezazadeh, H., Arshed, S., Bekir, A.: Optical solitons for the decoupled nonlinear Schrödinger equation using Jacobi elliptic approach. Commun. Theor. Phys. 73(7), 075003 (2021)
Zurück zum Zitat Samir, I., Badra, N., Seadawy, A.R., Ahmed, H.M., Arnous, A.H.: Exact wave solutions of the fourth order non-linear partial differential equation of optical fiber pulses by using different methods. Optik 230, 166313 (2021)ADSCrossRef Samir, I., Badra, N., Seadawy, A.R., Ahmed, H.M., Arnous, A.H.: Exact wave solutions of the fourth order non-linear partial differential equation of optical fiber pulses by using different methods. Optik 230, 166313 (2021)ADSCrossRef
Zurück zum Zitat Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Makhlouf, M.M., Althobaiti, Saad.: Optical solitons to birefringent fibers for coupled Radhakrishnan–Kundu–Lakshmanan model without four-wave mixing. Optical Quant. Electr. 53, 324 (2021) Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Makhlouf, M.M., Althobaiti, Saad.: Optical solitons to birefringent fibers for coupled Radhakrishnan–Kundu–Lakshmanan model without four-wave mixing. Optical Quant. Electr. 53, 324 (2021)
Zurück zum Zitat Shehata, M.S.: Extended Jacobian elliptic function expansion method and its applications for solving some nonlinear evolution equations in mathematical physics. Int. J. Comput. Appl. 109(12), 1–4 (2015) Shehata, M.S.: Extended Jacobian elliptic function expansion method and its applications for solving some nonlinear evolution equations in mathematical physics. Int. J. Comput. Appl. 109(12), 1–4 (2015)
Zurück zum Zitat Siddique, I., Jaradat, M.M., Zafar, A., Mehdi, K.B., Osman, M.S.: Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches. Results Phys. 28, 104557 (2021)CrossRef Siddique, I., Jaradat, M.M., Zafar, A., Mehdi, K.B., Osman, M.S.: Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches. Results Phys. 28, 104557 (2021)CrossRef
Zurück zum Zitat Yildirim, Y.: Optical solitons of Biswas–Arshed equation by modified simple equation technique. Optik 182, 986–994 (2019)ADSCrossRef Yildirim, Y.: Optical solitons of Biswas–Arshed equation by modified simple equation technique. Optik 182, 986–994 (2019)ADSCrossRef
Zurück zum Zitat Zayed, E.M.E., Alurrfi, K.A.E.: A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines. Chaos Solitons Fractals 78, 148–155 (2015a)ADSMathSciNetMATHCrossRef Zayed, E.M.E., Alurrfi, K.A.E.: A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines. Chaos Solitons Fractals 78, 148–155 (2015a)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Zayed, E., Alurrfi, K.: A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines. Chaos Solitons Fractals 78, 148–155 (2015b)ADSMathSciNetMATHCrossRef Zayed, E., Alurrfi, K.: A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines. Chaos Solitons Fractals 78, 148–155 (2015b)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Zayed, E.M.E., Shohib, R.M.A., Alngar, M.E.M., Yıldırım, Y.: Optical solitons in fiber Bragg gratings with Radhakrishnan–Kundu–Lakshmanan equation using two integration schemes. Optik 245, 167635 (2021)ADSCrossRef Zayed, E.M.E., Shohib, R.M.A., Alngar, M.E.M., Yıldırım, Y.: Optical solitons in fiber Bragg gratings with Radhakrishnan–Kundu–Lakshmanan equation using two integration schemes. Optik 245, 167635 (2021)ADSCrossRef
Zurück zum Zitat Zhang, R.F., Bilige, S.: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation. Nonlinear Dyn. 95(4), 3041–3048 (2019)MATHCrossRef Zhang, R.F., Bilige, S.: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation. Nonlinear Dyn. 95(4), 3041–3048 (2019)MATHCrossRef
Zurück zum Zitat Zhang, R.F., Li, M.C.: Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations. Nonlinear Dyn. 108, 521–531 (2022)CrossRef Zhang, R.F., Li, M.C.: Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations. Nonlinear Dyn. 108, 521–531 (2022)CrossRef
Zurück zum Zitat Zhang, R.F., Li, M.C., Yin, H.M.: Rogue wave solutions and the bright and dark solitons of the (3+ 1)-dimensional Jimbo–Miwa equation. Nonlinear Dyn. 103(1), 1071–1079 (2021)CrossRef Zhang, R.F., Li, M.C., Yin, H.M.: Rogue wave solutions and the bright and dark solitons of the (3+ 1)-dimensional Jimbo–Miwa equation. Nonlinear Dyn. 103(1), 1071–1079 (2021)CrossRef
Zurück zum Zitat Zhang, R.F., Li, M.C., Gan, J.Y., Li, Q., Lan, Z.Z.: Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method. Chaos Solitons Fractals 154, 111692 (2022)MathSciNetCrossRef Zhang, R.F., Li, M.C., Gan, J.Y., Li, Q., Lan, Z.Z.: Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method. Chaos Solitons Fractals 154, 111692 (2022)MathSciNetCrossRef
Metadaten
Titel
The dynamic behaviors of the Radhakrishnan–Kundu–Lakshmanan equation by Jacobi elliptic function expansion technique
verfasst von
Sibel Tarla
Karmina K. Ali
Resat Yilmazer
M. S. Osman
Publikationsdatum
01.05.2022
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 5/2022
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-022-03710-y

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