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Erschienen in: Optical and Quantum Electronics 5/2024

01.05.2024

New abundant analytical solutions of coupled nonlinear Schrödinger (FNSE) equation in fractal order arising in quantum mechanics

verfasst von: Maryam Alshahrani, Loubna Ouahid, M. A. Abdou, Sachin Kumar, Jameelah S. Al Shahrani

Erschienen in: Optical and Quantum Electronics | Ausgabe 5/2024

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Abstract

In this work, we investigate coupled space–time fractional nonlinear Schrödinger equation (FNSE) arising in physics. The FNSE can be utilized to explain non-relativistic quantum mechanical phenomena. With the aid of the conformable fractional derivative (CFD) and fractional complex transform (FCT), we implement the extensive direct algebraic approach (EDAA), the behaviors of some of the generated solutions are shown as 3D-graphics for various with different fractal orders. The optical soliton solutions that are bright periodic, kink bright and kink-bright periodic are among these precise solutions. The acquired results demonstrate the simplicity, effectiveness, and capacity to produce additional kinds of exact solutions of these proposed methods, which are useful in deciphering the intricate physical interpretation of space–time FNSE.

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Literatur
Zurück zum Zitat Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)MathSciNet Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)MathSciNet
Zurück zum Zitat Abdou, M.A., Owyed, S., Saha Ray, S., Inc, M., Chu, Y.M., Ouahid, L.: Fractal Ion acoustic waves of the space-time fractional three dimensional KP equation. Adv. Math. Phys. 2020, 8323148 (2020)MathSciNet Abdou, M.A., Owyed, S., Saha Ray, S., Inc, M., Chu, Y.M., Ouahid, L.: Fractal Ion acoustic waves of the space-time fractional three dimensional KP equation. Adv. Math. Phys. 2020, 8323148 (2020)MathSciNet
Zurück zum Zitat Abdou, M.A., Ouahid, L., Al Shahrani, J.S., Owyed, S.: Novel analytical techniques for HIV-1 infection of CD4+T-cells on fractional order in mathematical biology. Indian J. Phys. 97, 2319–2325 (2023a)ADS Abdou, M.A., Ouahid, L., Al Shahrani, J.S., Owyed, S.: Novel analytical techniques for HIV-1 infection of CD4+T-cells on fractional order in mathematical biology. Indian J. Phys. 97, 2319–2325 (2023a)ADS
Zurück zum Zitat Abdou, M.A., Ouahid, L., Kumar, S.: Plenteous specific analytical solutions for new extended deoxyribonucleic acid (DNA) model arising in mathematical biology. Mod. Phys. Lett. B 37(34), 2350173 (2023b)ADSMathSciNet Abdou, M.A., Ouahid, L., Kumar, S.: Plenteous specific analytical solutions for new extended deoxyribonucleic acid (DNA) model arising in mathematical biology. Mod. Phys. Lett. B 37(34), 2350173 (2023b)ADSMathSciNet
Zurück zum Zitat Ahmad, J., Rani, S.: Study of soliton solutions with different wave formations to model of nonlinear Schrödinger equation with mixed derivative and applications. Opt. Quant. Electron. 55, 1195 (2023) Ahmad, J., Rani, S.: Study of soliton solutions with different wave formations to model of nonlinear Schrödinger equation with mixed derivative and applications. Opt. Quant. Electron. 55, 1195 (2023)
Zurück zum Zitat Akbar, M.A., Wazwaz, A.M., Mahmud, F., Baleanu, D., Roy, R., Barman, H.K., Mahmoud, W., Sharif, M.A.A., Osman, M.S.: Dynamical behavior of solitons of the perturbed nonlinear Schrodinger equation and microtubules through the generalized Kudryashov scheme. Results Phys. 43, 106079 (2022) Akbar, M.A., Wazwaz, A.M., Mahmud, F., Baleanu, D., Roy, R., Barman, H.K., Mahmoud, W., Sharif, M.A.A., Osman, M.S.: Dynamical behavior of solitons of the perturbed nonlinear Schrodinger equation and microtubules through the generalized Kudryashov scheme. Results Phys. 43, 106079 (2022)
Zurück zum Zitat Akbar, M.A., Abdullah, F.A., Islam, M.D.T., Al Sharif, M.A., Osman, M.S.: Newsolutions of the soliton type of shallow water waves and superconductivity models. Res. Phys. 44, 106180 (2023) Akbar, M.A., Abdullah, F.A., Islam, M.D.T., Al Sharif, M.A., Osman, M.S.: Newsolutions of the soliton type of shallow water waves and superconductivity models. Res. Phys. 44, 106180 (2023)
Zurück zum Zitat Akram, S., Ahmad, J., Ur-Rehman, S., Sarwar, S., Ali, A.: Dynamics of soliton solutions in optical fibers modeled by perturbed nonlinear Schrodinger equation and stability analysis. Opt. Quantum Electron. 55, 450 (2023) Akram, S., Ahmad, J., Ur-Rehman, S., Sarwar, S., Ali, A.: Dynamics of soliton solutions in optical fibers modeled by perturbed nonlinear Schrodinger equation and stability analysis. Opt. Quantum Electron. 55, 450 (2023)
Zurück zum Zitat Al Alwan, B., Abu Bakar, M., Faridi, W.A., Turcu, A.C., Akgül, A., Sallah, M.: The propagating exact solitary waves formation of generalized Calogero–Bogoyavlenskii–Schiff equation with robust computational approaches. Fractal Fract. 7, 191 (2023) Al Alwan, B., Abu Bakar, M., Faridi, W.A., Turcu, A.C., Akgül, A., Sallah, M.: The propagating exact solitary waves formation of generalized Calogero–BogoyavlenskiiSchiff equation with robust computational approaches. Fractal Fract. 7, 191 (2023)
Zurück zum Zitat Ala, V.: New exact solutions of space-time fractional Schrodinger–Hirota equation. Bull. Karaganda Univer. Math. Ser. 107, 3 (2022) Ala, V.: New exact solutions of space-time fractional Schrodinger–Hirota equation. Bull. Karaganda Univer. Math. Ser. 107, 3 (2022)
Zurück zum Zitat Ala, V.: Exact solutions of nonlinear time fractional schrödinger equation with beta-derivative. Fundam. Contemp. Math. Sci. 4(1), 1–8 (2023)MathSciNet Ala, V.: Exact solutions of nonlinear time fractional schrödinger equation with beta-derivative. Fundam. Contemp. Math. Sci. 4(1), 1–8 (2023)MathSciNet
Zurück zum Zitat Ala, V., Shaikhova, G.: Analytical solutions of nonlinear beta fractional schrödinger equation via sine-cosine method. Lobachevskii J. Math. 43(11), 3033–3038 (2022)MathSciNet Ala, V., Shaikhova, G.: Analytical solutions of nonlinear beta fractional schrödinger equation via sine-cosine method. Lobachevskii J. Math. 43(11), 3033–3038 (2022)MathSciNet
Zurück zum Zitat Alabedalhadi, M.: Exact travelling wave solutions for nonlinear system of spatiotemporal fractionlquantum mechanics equations. Alex. Eng. J. 61, 1033–1044 (2022) Alabedalhadi, M.: Exact travelling wave solutions for nonlinear system of spatiotemporal fractionlquantum mechanics equations. Alex. Eng. J. 61, 1033–1044 (2022)
Zurück zum Zitat Alanazi, M.M., Ouahid, L., Al Shahrani, J.S., Abdou, M.A., Kumar, S.: Novel soliton solutions to the Atangana Baleanu (AB) fractional for ion sound and Langmuir waves (ISALWs) equations. Opt. Quantum Electron. 55, 462 (2023) Alanazi, M.M., Ouahid, L., Al Shahrani, J.S., Abdou, M.A., Kumar, S.: Novel soliton solutions to the Atangana Baleanu (AB) fractional for ion sound and Langmuir waves (ISALWs) equations. Opt. Quantum Electron. 55, 462 (2023)
Zurück zum Zitat Ali, A., Ahmad, J., Javed, S.: Solitary wave solutions for the originating waves that propagate of the fractional Wazwaz–Benjamin–Bona–Mahony system. Alex. Eng. J. 69, 121–133 (2023) Ali, A., Ahmad, J., Javed, S.: Solitary wave solutions for the originating waves that propagate of the fractional Wazwaz–Benjamin–Bona–Mahony system. Alex. Eng. J. 69, 121–133 (2023)
Zurück zum Zitat Alqhtani, M., Saad, K.M., Shah, R., Hamanah, W.M.: Discovering novel soliton solutions for (3+1)-modified fractional Zakharov–Kuznetsov equation in electrical engineering through an analytical approach. Opt. Quant. Electron. 55, 1149 (2023) Alqhtani, M., Saad, K.M., Shah, R., Hamanah, W.M.: Discovering novel soliton solutions for (3+1)-modified fractional Zakharov–Kuznetsov equation in electrical engineering through an analytical approach. Opt. Quant. Electron. 55, 1149 (2023)
Zurück zum Zitat Aniqa, A., Ahmad, J.: Soliton solution of fractional Sharma–Tasso–Olever equation via an efficient (G′/G)-expansion method. Ain Shams Eng. J. 13, 101528 (2022) Aniqa, A., Ahmad, J.: Soliton solution of fractional Sharma–Tasso–Olever equation via an efficient (G′/G)-expansion method. Ain Shams Eng. J. 13, 101528 (2022)
Zurück zum Zitat Zulfiqar, A., Ahmad, J.: Soliton solutions of fractional modified unstable Schrödinger equation using Exp-function method. Results Phys. 19, 103476 (2020a) Zulfiqar, A., Ahmad, J.: Soliton solutions of fractional modified unstable Schrödinger equation using Exp-function method. Results Phys. 19, 103476 (2020a)
Zurück zum Zitat Faridi, W.A., Yusuf, A., Akgül, A., Tawfiq, F.M., Tchier, F., Al-deiakeh, R., Sulaiman, T.A., Hassan, A.M., Ma, W.X.: The computation of Lie point symmetry generators, modulational instability classification of conserved quantities, and explicit power series solutions of the coupled system. Results Phys. 54, 107126 (2023a) Faridi, W.A., Yusuf, A., Akgül, A., Tawfiq, F.M., Tchier, F., Al-deiakeh, R., Sulaiman, T.A., Hassan, A.M., Ma, W.X.: The computation of Lie point symmetry generators, modulational instability classification of conserved quantities, and explicit power series solutions of the coupled system. Results Phys. 54, 107126 (2023a)
Zurück zum Zitat Faridi, W.A., Bakar, M.A., Myrzakulova, Z., Myrzakulova, R., Akgul, A., El Din, S.M.: The formation of solitary wave solutions and their propagation for Kuralay equation. Results Phys. 52, 106774 (2023ab) Faridi, W.A., Bakar, M.A., Myrzakulova, Z., Myrzakulova, R., Akgul, A., El Din, S.M.: The formation of solitary wave solutions and their propagation for Kuralay equation. Results Phys. 52, 106774 (2023ab)
Zurück zum Zitat Faridi, W.A., Asjad, M.I., Jhangeer, A., Yusuf, A., Sulaiman, T.A.: The weakly non-linear waves propagation for Kelvin-Helmholtz instability in the magnetohydrodynamics flow impelled by fractional theory. Opt. Quant. Electron. 55, 172 (2023bc) Faridi, W.A., Asjad, M.I., Jhangeer, A., Yusuf, A., Sulaiman, T.A.: The weakly non-linear waves propagation for Kelvin-Helmholtz instability in the magnetohydrodynamics flow impelled by fractional theory. Opt. Quant. Electron. 55, 172 (2023bc)
Zurück zum Zitat Faridi, W.A., Bakar, M.A., Akgül, A., Abd El-Rahman, M., El Din, S.M.: Exact fractional soliton solutions of thin-film ferroelectric material equation by analytical approaches. Alex. Eng. J. 78, 483–497 (2023d) Faridi, W.A., Bakar, M.A., Akgül, A., Abd El-Rahman, M., El Din, S.M.: Exact fractional soliton solutions of thin-film ferroelectric material equation by analytical approaches. Alex. Eng. J. 78, 483–497 (2023d)
Zurück zum Zitat Faridi, W.A., Yusuf, A., Akgul, A., Tawfiq, F.M.O., Tchier, F., Al-deiakeh, R., Sulaiman, T.A., Hassan, A.M., Ma, W.-X.: The computation of Lie point symmetry generators, modulational instability classification of conserved quantities, and explicit power series solutions of the coupled system. Results Phys. 54, 107126 (2023de) Faridi, W.A., Yusuf, A., Akgul, A., Tawfiq, F.M.O., Tchier, F., Al-deiakeh, R., Sulaiman, T.A., Hassan, A.M., Ma, W.-X.: The computation of Lie point symmetry generators, modulational instability classification of conserved quantities, and explicit power series solutions of the coupled system. Results Phys. 54, 107126 (2023de)
Zurück zum Zitat Faridi, W.A., Hussain, G., Myrzakulova, Z., Myrzakulov, R., Akinyemi, L.: Formation of optical soliton wave profles of Shynaray-IIA equation via two improved techniques: a comparative study. Opt. Quant. Electron. 56, 132 (2024)ADS Faridi, W.A., Hussain, G., Myrzakulova, Z., Myrzakulov, R., Akinyemi, L.: Formation of optical soliton wave profles of Shynaray-IIA equation via two improved techniques: a comparative study. Opt. Quant. Electron. 56, 132 (2024)ADS
Zurück zum Zitat Fendzi-Donfack, E., Tala-Tebue, E., Inc, M., Kenfack-Jiotsa, A., Nguenang, J.P., Nana, L.: Dynamical behaviours and fractional alphabetical-exotic solitons in a coupled nonlinear electrical transmission lattice including wave obliqueness. Opt. Quant. Electron. 55, 35 (2023) Fendzi-Donfack, E., Tala-Tebue, E., Inc, M., Kenfack-Jiotsa, A., Nguenang, J.P., Nana, L.: Dynamical behaviours and fractional alphabetical-exotic solitons in a coupled nonlinear electrical transmission lattice including wave obliqueness. Opt. Quant. Electron. 55, 35 (2023)
Zurück zum Zitat Ganaini, E.S.: Solitons and other solutions to a new coupled nonlinear Schrödinger type equation. J. Egypt. Math. Soc. 25, 19–27 (2017) Ganaini, E.S.: Solitons and other solutions to a new coupled nonlinear Schrödinger type equation. J. Egypt. Math. Soc. 25, 19–27 (2017)
Zurück zum Zitat Ghanbari, B.: “Abundant soliton solutions for the Hirota–Maccari equation via the generalized exponential rational function method. Mod. Phys. Lett. B 33(09), 1950106 (2019)ADSMathSciNet Ghanbari, B.: “Abundant soliton solutions for the Hirota–Maccari equation via the generalized exponential rational function method. Mod. Phys. Lett. B 33(09), 1950106 (2019)ADSMathSciNet
Zurück zum Zitat Ghanbari, B., Akgül, A.: Abundant new analytical and approximate solutions to the generalized Schamel equation. Phys. Scr. 95, 075201 (2020)ADS Ghanbari, B., Akgül, A.: Abundant new analytical and approximate solutions to the generalized Schamel equation. Phys. Scr. 95, 075201 (2020)ADS
Zurück zum Zitat Ghanbari, B., Baleanu, D.: New solutions of Gardner’s equation using two analytical methods. Front. Phys. 7, 202 (2019) Ghanbari, B., Baleanu, D.: New solutions of Gardner’s equation using two analytical methods. Front. Phys. 7, 202 (2019)
Zurück zum Zitat Ghanbari, B., Baleanu, D.: New optical solutions of the fractional Gerdjikov–Ivanov equation with conformable derivative. Front. Phys. 8, 2020 (2020) Ghanbari, B., Baleanu, D.: New optical solutions of the fractional Gerdjikov–Ivanov equation with conformable derivative. Front. Phys. 8, 2020 (2020)
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 (2019a)ADSMathSciNet Ghanbari, B., Gómez-Aguilar, J.F.: Optical soliton solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation. Mod. Phys. Lett. B 33(32), 1950402 (2019a)ADSMathSciNet
Zurück zum Zitat Ghanbari, B., Gómez-Aguilar, J.F.: New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative. Mod. Phys. Lett. B 33(20), 1950235 (2019b)ADS Ghanbari, B., Gómez-Aguilar, J.F.: New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative. Mod. Phys. Lett. B 33(20), 1950235 (2019b)ADS
Zurück zum Zitat Ghanbari, B., Kuo, C.-K.: New exact wave solutions of the variable-coefficient (1 + 1)-dimensional Benjamin-Bona-Mahony and (2 + 1)-dimensional asymmetric Nizhnik–Novikov–Veselov equations via the generalized exponential rational function method. Eur. Phys. J. plus 134, 334 (2019) Ghanbari, B., Kuo, C.-K.: New exact wave solutions of the variable-coefficient (1 + 1)-dimensional Benjamin-Bona-Mahony and (2 + 1)-dimensional asymmetric Nizhnik–Novikov–Veselov equations via the generalized exponential rational function method. Eur. Phys. J. plus 134, 334 (2019)
Zurück zum Zitat Ghanbari, B., Baleanu, D., Al Qurashi, M.: New exact solutions of the generalized Benjamin–Bona–Mahony equation. Symmetry 11(1), 19 (2019) Ghanbari, B., Baleanu, D., Al Qurashi, M.: New exact solutions of the generalized Benjamin–Bona–Mahony equation. Symmetry 11(1), 19 (2019)
Zurück zum Zitat Hamid, I., Kumar, S.: Symbolic computation and Novel solitons, traveling waves and soliton-like solutions for the highly nonlinear (2+1)-dimensional Schrödinger equation in the anomalous dispersion regime via newly proposed modified approach. Opt. Quant. Electron. 55(9), 755 (2023) Hamid, I., Kumar, S.: Symbolic computation and Novel solitons, traveling waves and soliton-like solutions for the highly nonlinear (2+1)-dimensional Schrödinger equation in the anomalous dispersion regime via newly proposed modified approach. Opt. Quant. Electron. 55(9), 755 (2023)
Zurück zum Zitat Hoan, L.V.C., Owyed, S., Inc, M., Ouahid, L., Abdou, M.A., Chu, Y.-M.: New explicit optical solitons of fractional nonlinear evolution equation via three different methods. Results Phys. 18, 103209 (2020) Hoan, L.V.C., Owyed, S., Inc, M., Ouahid, L., Abdou, M.A., Chu, Y.-M.: New explicit optical solitons of fractional nonlinear evolution equation via three different methods. Results Phys. 18, 103209 (2020)
Zurück zum Zitat Islam, M.D.T., Akbar, M.D.A., Gómez-Aguilar, J.F., Bonyah, E., Fernandez-Anaya, G.: Assorted soliton structures of solutions for fractional nonlinear Schrodinger types evolution equations. J. Ocean Eng. Sci. 7, 528–535 (2022) Islam, M.D.T., Akbar, M.D.A., Gómez-Aguilar, J.F., Bonyah, E., Fernandez-Anaya, G.: Assorted soliton structures of solutions for fractional nonlinear Schrodinger types evolution equations. J. Ocean Eng. Sci. 7, 528–535 (2022)
Zurück zum Zitat Islam, M.D.T., Ryehan, S., Abdullah, F.A., Gómez-Aguilar, J.F.: The effect of Brownian motion and noise strength on solutions of stochastic Bogoyavlenskii model alongside conformable fractional derivative. Optik 287, 171140 (2023)ADS Islam, M.D.T., Ryehan, S., Abdullah, F.A., Gómez-Aguilar, J.F.: The effect of Brownian motion and noise strength on solutions of stochastic Bogoyavlenskii model alongside conformable fractional derivative. Optik 287, 171140 (2023)ADS
Zurück zum Zitat Khalil, R., Horani, M.A., Yousef, A., Sababheh, M.A.: New definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNet Khalil, R., Horani, M.A., Yousef, A., Sababheh, M.A.: New definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNet
Zurück zum Zitat Khater, M., Ghanbari, B.: On the solitary wave solutions and physical characterization of gas diffusion in a homogeneous medium via some efficient techniques. Eur. Phys. J. 136, 447 (2021) Khater, M., Ghanbari, B.: On the solitary wave solutions and physical characterization of gas diffusion in a homogeneous medium via some efficient techniques. Eur. Phys. J. 136, 447 (2021)
Zurück zum Zitat Kılıç, S.ŞŞ, Çelik, E., Bulut, H.: Solitary wave solutions to some nonlinear conformable partial differential equations. Opt. Quant. Electron. 55, 693 (2023) Kılıç, S.ŞŞ, Çelik, E., Bulut, H.: Solitary wave solutions to some nonlinear conformable partial differential equations. Opt. Quant. Electron. 55, 693 (2023)
Zurück zum Zitat Kumar, S., Hamid, I., Abdou, M.A.: Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in (3+1)-dimensions with gas bubbles in hydrodynamics and fluids. J. Ocean Eng. Sci. 8, 91–102 (2023) Kumar, S., Hamid, I., Abdou, M.A.: Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in (3+1)-dimensions with gas bubbles in hydrodynamics and fluids. J. Ocean Eng. Sci. 8, 91–102 (2023)
Zurück zum Zitat Ma, Y., Geng, X.: A coupled nonlinear Schrödinger type equation and its explicit solutions. Chaos Soliton Fract. 42, 2949–2953 (2009)ADS Ma, Y., Geng, X.: A coupled nonlinear Schrödinger type equation and its explicit solutions. Chaos Soliton Fract. 42, 2949–2953 (2009)ADS
Zurück zum Zitat Mirzazadeh, M., Akinyemi, L., Senol, M., Hosseini, K.: A variety of solitons to sixth-order dispersive (3+1)-dimensional nonlinear time-fractional Schrödinger equation with cubic-septic nonlinearities. Optik 241, 166318 (2021)ADS Mirzazadeh, M., Akinyemi, L., Senol, M., Hosseini, K.: A variety of solitons to sixth-order dispersive (3+1)-dimensional nonlinear time-fractional Schrödinger equation with cubic-septic nonlinearities. Optik 241, 166318 (2021)ADS
Zurück zum Zitat Ouahid, L., Owyed, S., Abdou, M.A., Alshehri, N.A., Elagan, S.K.: New optical soliton solutions via generalized Kudryashov’s scheme for Ginzburg–Landau equation in fractal order. Alex. Eng. J. 60(6), 5495–5510 (2021) Ouahid, L., Owyed, S., Abdou, M.A., Alshehri, N.A., Elagan, S.K.: New optical soliton solutions via generalized Kudryashov’s scheme for Ginzburg–Landau equation in fractal order. Alex. Eng. J. 60(6), 5495–5510 (2021)
Zurück zum Zitat Ozdemir, N., Esen, H., Secer, A., Bayram, M., Yusuf, A., Sulaiman, T.A.: Optical solitons and other solutions to the Hirota-Maccari system with conformable, M-truncated and beta derivatives. Mod. Phys. Lett. B 36(11), 2150625 (2022)ADSMathSciNet Ozdemir, N., Esen, H., Secer, A., Bayram, M., Yusuf, A., Sulaiman, T.A.: Optical solitons and other solutions to the Hirota-Maccari system with conformable, M-truncated and beta derivatives. Mod. Phys. Lett. B 36(11), 2150625 (2022)ADSMathSciNet
Zurück zum Zitat Rani, A., Zulfiqar, A., Ahmad, J., Ul Hassan, Q.M.: New soliton wave structures of fractional Gilson–Pickering equation using tanh–coth method and their application. Results Phys. 29, 104724 (2021) Rani, A., Zulfiqar, A., Ahmad, J., Ul Hassan, Q.M.: New soliton wave structures of fractional Gilson–Pickering equation using tanh–coth method and their application. Results Phys. 29, 104724 (2021)
Zurück zum Zitat Shi, L., Zhou, X.: Exact solutions of a coupled space-time fractional nonlinear Schrödinger type equation in quantum mechanics. Results Phys. 42, 105967 (2022) Shi, L., Zhou, X.: Exact solutions of a coupled space-time fractional nonlinear Schrödinger type equation in quantum mechanics. Results Phys. 42, 105967 (2022)
Zurück zum Zitat Tozar, A., Kurt, A., Tasbozan, O.: New wave solutions of an integrable dispersive wave equation with a fractional time derivative arising in ocean engineering models. Kuwait J. Sci. 47(2), 22–23 (2020) Tozar, A., Kurt, A., Tasbozan, O.: New wave solutions of an integrable dispersive wave equation with a fractional time derivative arising in ocean engineering models. Kuwait J. Sci. 47(2), 22–23 (2020)
Zurück zum Zitat Ur-Rehman, S., Bilal, M., Ahmad, J.: New exact solitary wave solutions for the 3D-FWBBM model in arising shallow water waves by two analytical methods. Results Phys. 25, 104230 (2021) Ur-Rehman, S., Bilal, M., Ahmad, J.: New exact solitary wave solutions for the 3D-FWBBM model in arising shallow water waves by two analytical methods. Results Phys. 25, 104230 (2021)
Zurück zum Zitat Vahidi, J., Zabihi, A., Rezazadeh, H., Ansari, R.: New extended direct algebraic method for the resonant nonlinear Schrödinger equation with Kerr law nonlinearity. Optik 227, 165936 (2021)ADS Vahidi, J., Zabihi, A., Rezazadeh, H., Ansari, R.: New extended direct algebraic method for the resonant nonlinear Schrödinger equation with Kerr law nonlinearity. Optik 227, 165936 (2021)ADS
Zurück zum Zitat Wang, B.H., Lu, P.H., Dai, C.Q., Chen, Y.X.: Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrödinger equation. Results Phys. 17, 103036 (2020) Wang, B.H., Lu, P.H., Dai, C.Q., Chen, Y.X.: Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrödinger equation. Results Phys. 17, 103036 (2020)
Zurück zum Zitat Xu, Y., Feng, Y., Jiang, J.: Exact solutions of the fractional resonant nonlinear Schrödinger equation. Opt. Quant. Electron. 55, 1208 (2023) Xu, Y., Feng, Y., Jiang, J.: Exact solutions of the fractional resonant nonlinear Schrödinger equation. Opt. Quant. Electron. 55, 1208 (2023)
Zurück zum Zitat Yokuş, A., Durur, H., Duran, S., Islam, M.D.T.: Ample felicitous wave structures for fractional foam drainage equation modeling for fluid-flow mechanism. Comput. Appl. Math. 41, 174 (2022)MathSciNet Yokuş, A., Durur, H., Duran, S., Islam, M.D.T.: Ample felicitous wave structures for fractional foam drainage equation modeling for fluid-flow mechanism. Comput. Appl. Math. 41, 174 (2022)MathSciNet
Zurück zum Zitat Zhou, G.Z., Dai, C.Q.: Nonautonomous soliton solutions of variable-coefficient fractional nonlinear Schrödinger equation. Appl. Math. Lett. 106, 106365 (2020)MathSciNet Zhou, G.Z., Dai, C.Q.: Nonautonomous soliton solutions of variable-coefficient fractional nonlinear Schrödinger equation. Appl. Math. Lett. 106, 106365 (2020)MathSciNet
Zurück zum Zitat Zulfiqar, A., Ahmad, J.: Soliton solutions of fractional modified unstable Schrödinger equation using Exp-function method. Results Phys. 19, 103476 (2020b) Zulfiqar, A., Ahmad, J.: Soliton solutions of fractional modified unstable Schrödinger equation using Exp-function method. Results Phys. 19, 103476 (2020b)
Metadaten
Titel
New abundant analytical solutions of coupled nonlinear Schrödinger (FNSE) equation in fractal order arising in quantum mechanics
verfasst von
Maryam Alshahrani
Loubna Ouahid
M. A. Abdou
Sachin Kumar
Jameelah S. Al Shahrani
Publikationsdatum
01.05.2024
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 5/2024
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-024-06378-8

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