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New optical soliton solutions for the (2+1) Fokas system via three techniques

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Abstract

The nonlinear Schrödinger equation’s natural protraction, the (2+1) Fokas system, illustrates how a pulse moves across monomode optical fibers. Three efficient methods the Sardar sub-equation approach, the Bernoulli sub-ODE method, and the generic Kudryashov’s method are used in this study to offer various families of solutions. Several sorts of function solutions, including those for hyperbolic, trigonometric, power, exponential, and rational functions, are provided by our suggested approaches. In order to highlight the many solutions found, numerous graphs are given toward the conclusion of the text.

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References

  • Akinyemi, L., Senol, M., Az-Zobi, E., Veeresha, P., Akpan, U.: Novel soliton solutions of four sets of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili-like equations. Modern Phys. Lett. B 36(01), 2150530 (2022)

    MathSciNet  ADS  Google Scholar 

  • Ali, K.K., Mehanna, M.S.: On some new analytical solutions to the (2+1)-dimensional nonlinear electrical transmission line model. Eur. Phys. J. Plus 137–280, 1–12 (2022)

    ADS  Google Scholar 

  • Ali, M.Y., Hafez, M.G., Chowdury, M.K.H., Akter, M.T.: Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada–Kotera Equation via the Generalized \(\exp (-\phi (\xi ))\)Expansion Method. J. Appl. Math. Phys. 4, 262-271 (2016)

    Google Scholar 

  • Ali, K.K., Mehanna, M.S., Akbar, M.A., Chakrabarti, P.: Analytical soliton solutions of the coupled RadhakrishnanKundu-Lakshmanan equation via three techniques. J. Math. 2022, 8419403 (2022)

    Google Scholar 

  • Almusawa, H., Ali, K.K., Wazwaz, A.M., Mehanna, M.S., Baleanu, D., Osman, M.S.: Protracted study on a real physical phenomenon generated by media inhomogeneities. Results Phys. 31, 104933 (2021)

    Google Scholar 

  • Altawallbeh, Z., Az-Zo’bi, E., Alleddawi, A.O.: Mehmet şenol Lanre Akinyemi Novel liquid crystals model and its nematicons. Opt. Q. Electron. 54, 861 (2022)

    Google Scholar 

  • Attia, R.A., Baleanu, D., Lu, D., Khater, M.M., Ahmed, E.S.: Computational and numerical simulations for the deoxyribonucleic acid (DNA) model. Disc. Cont. Dyn. Syst. 14, 3459-3478 (2021)

    MathSciNet  MATH  Google Scholar 

  • Az-Zobi, E.A., AlZo’ubi, W.A., Akinyemi, L., Senol, M., Alsaraireh, I.W., Mamat, M.: Abundant closed-form solitons for time-fractional integro—differential equation in fluid dynamics. Opt. Q. Electron. 53, 1–16 (2021)

    Google Scholar 

  • Az-Zo’bi, E., Akinyemi, L., Alleddawi, A.O.: Construction of optical solitons for conformable generalized model in nonlinear media. Mod. Phys. Lett. B 35, (24) 2150409 (2021)

    MathSciNet  ADS  Google Scholar 

  • Cao, Y., Rao, J., Mihalache, D., He, J.: Semi-rational solutions for the (2+1)-dimensional nonlocal Fokas system. Appl. Math. Lett. 80, 27–34 (2018)

    MathSciNet  MATH  Google Scholar 

  • Cinar, M., Onder, I., Secer, A., Sulaiman, T.A., Yusuf, A., Bayram, M.: Optical solitons of the (2+ 1)-dimensional Biswas–Milovic equation using modified extended tanh-function method. Optik 12, 245 (2021)

    Google Scholar 

  • Feng, Q.: Traveling wave solution of (3+1) dimensional potential-YTSF equation by Bernoulli Sub-ODE method. Adv. Mater. Res. , 212 403–408 (2012)

    Google Scholar 

  • Fokas, A.S.: On the simplest integrable equation in 2+1. Inverse Probl. 10, L19-22 (1994)

    MathSciNet  ADS  Google Scholar 

  • Hamood-Ur-Rahman, A., Muhammad, I., Munawar, N., Parvaneh, F., Muhammad, T., Hamoud, A.A., Emadifar, H., Hamasalh, F.K., Azizi, H., Khadem, M.: Traveling wave solutions to the Boussinesq equation via Sardar sub-equation technique. AIMS Math. 7(6), 11134–11149 (2022)

    MathSciNet  Google Scholar 

  • Ismael, H.F., Murad, M.A.S., Bulut, H.: Various exact wave solutions for KDV equation with time-variable coefficients. J. Ocean Eng. Sci. 75, 409-418 (2021)

    Google Scholar 

  • Ismael, H.F., Ma, W.X., Bulut, H.: Dynamics of soliton and mixed lump-soliton waves to a generalized Bogoyavlensky– Konopelchenko equation. Phys. Scr. 96, 035225 (2021)

    ADS  Google Scholar 

  • Ji-Guang, R.A.O., Li-Hong, W.A.N.G.: ZHANG Yu, and HE Jing-Song, Rational Solutions for the Fokas System. Commun. Theoret. Phys. 64, 605–618 (2015)

    ADS  Google Scholar 

  • Kaur, L., Wazwaz, A.-M.: Dynamical Analysis of Lump Solutions for (3 + 1) dimensional generalized KP-Boussinesq equation and Its Dimensionally Reduced equations. Phys. Scr. 93, 075203 (2018)

    ADS  Google Scholar 

  • Kaur, L., Wazwaz, A.-M.: Bright- Dark Lump wave solutions for a new form of the \((3+1)\)-dimensional BKP-Boussinesq equation. Romanian Rep. Phys. 71, 102 (2019)

    Google Scholar 

  • Kaur, L., Wazwaz, A.-M.: Lump, breather and solitary wave solutions to new reduced form of the generalized BKP equation. Int. J. Numer. Meth. Heat Fluid Flow 29(2), 569–579 (2019)

    Google Scholar 

  • Kaur, L., Wazwaz, A.-M.: Dynamical analysis of soliton solutions for space-time fractional Calogero–Degasperis and Sharma–Tasso–Olver equations. Romanian Rep. Phys. 74, 108 (2022)

    Google Scholar 

  • Khalil, T.A., Badra, N., Ahmed, H.M., Rabie, W.B.: Optical solitons and other solutions for coupled system of nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index by Jacobi elliptic function expansion method. Optik 253, 168540 (2022)

    ADS  Google Scholar 

  • Lan, L., Chen, A.-H., Zhou, A.-J.: Solitary wave, lump and their interactional solutions of the (3+1)-dimensional nonlinear evolution equation. Phys. Scr. 94, 105211 (2019)

    ADS  Google Scholar 

  • Maimistov, A.I.: Solitons in nonlinear optics. Q. Electron. 40(9), 756–781 (2010)

    ADS  Google Scholar 

  • Nisar, K.S., Ali, K.K., Inc, M., Mehanna, M.S., Rezazadeh, H., Akinyemi, L.: New solutions for the generalized resonant nonlinear Schrödinger equation. Results Phys. 33, 458 (2022)

    Google Scholar 

  • Onder, I., Secer, A., Ozisik, M., Bayram, M.: On the optical soliton solutions of Kundu-Mukherjee–Naskar equation via two different analytical methods. Opt. Int. J. Light Electron. Opt. 257, 168761 (2022)

    Google Scholar 

  • Peng, W.-Q., Tian, S.-F., Zhang, T.-T.: Dynamics of breather waves and higher-order rogue waves in a coupled nonlinear Schrödinger equation. Europhys. Lett. 123, 50005 (2018)

    ADS  Google Scholar 

  • Prinari, B., Vitale, F., Biondini, G.: Dark-bright soliton solutions with nontrivial polarization interactions for the three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions. J. Math. Phys. 56, 475–533 (2015)

    MATH  Google Scholar 

  • Rahman, R.U., Al-Maaitah, A.F., Qousini, M., Az-Zobi, E.A., Eldin, S.M., Abuzar, M.: New soliton solutions and modulation instability analysis of fractional Huxley equation. Results Phys. 44, 106163 (2023)

    Google Scholar 

  • Rao, J., Mihalache, D., Cheng, Y., He, J.: Lump-soliton solutions to the Fokas system. Phys. Lett. A 383(11), 1138–42 (2019)

    MathSciNet  MATH  ADS  Google Scholar 

  • Rezazadeh, H., Inc, M., Baleanu, D.: New solitary wave solutions for variants of (3+1)-dimensional Wazwaz–Benjamin–Bona–Mahony equations. Front. Phys. 8, 4586 (2020)

    Google Scholar 

  • Rezazadeh, H., Ullah, N., Akinyemi, L., Shah, A., Mirhosseini-Alizamin, S.M., Chu, Y.M., Ahmad, H.: Optical soliton solutions of the generalized non-autonomous nonlinear-dinger equations by the new Kudryashov–slashhcs method. Results Phys. 24, 104179 (2021)

    Google Scholar 

  • Taghizadeh, N., Akbari, M., Esmaeelnejhad, P.: Application of Bernoulli Sub-ODE method for finding travelling wave solutions of schrodinger equation power law nonlinearity. Int. J. 12(1), 596–603 (2017)

    MathSciNet  MATH  Google Scholar 

  • Tahani, A.: Alrebdi, Nauman Raza, Saima Arshed, Abdel-Haleem Abdel–Aty, New solitary wave patterns of Fokas? System arising in monomode fiber communication systems. Opt. Quant. Electron. 54, 712 (2022)

    Google Scholar 

  • Tao, G., Sabi’u, J., Nestor, S., El-Shiekh, R.M., Akinyemi, L., Az-Zo’bi, E., Betchewe, G.: Dynamics of a new class of solitary wave structures in telecommunications systems via a (2+1)-dimensional nonlinear transmission line. Mod. Phys. Lett. B 36, (19) 2150596 (2022)

    MathSciNet  ADS  Google Scholar 

  • Tarla, S., Ali, K.K., Sun, T.C., Yilmazer, R., Osman, M.S.: Nonlinear pulse propagation for novel optical solitons modeled by Fokas system in monomode optical fibers. Results Phys. 36, 105381 (2022)

    Google Scholar 

  • Wang, K.J.: Abundant exact soliton solutions to the Fokas system. Optik 249, 168265 (2022)

    ADS  Google Scholar 

  • Wang, K.J., Wang, G.D.: Variational theory and new abundant solutions to the (1+2)-dimensional chiral nonlinear Schrödinger equation in optics. Phys. Lett. A 412, 127588 (2021)

    MATH  Google Scholar 

  • Wang, L., Luan, Z., Zhou, Q., Biswas, A., Alzahrani, A.K., Liu, W.: Effects of dispersion terms on optical soliton propagation in a lossy fiber system. Nonlinear Dyn. 104(1), 629–37 (2021)

    Google Scholar 

  • Wang, K.J., Liu, J.H., Wu, J.: Soliton solutions to the Fokas system arising in monomode optical fibers. Optik 251, 168319 (2022)

    ADS  Google Scholar 

  • Xu, J.H.: Unified, improved matrix upper bound on the solution of the continuous coupled algebraic Riccati equation. J. Franklin I. 350, 1634–3648 (2013)

    MathSciNet  MATH  Google Scholar 

  • Zhang, P.-L., Wang, K.-J.: Abundant optical soliton structures to the Fokas system arising in monomode optical fibers. Open Phys. 20, 493–506 (2022)

    Google Scholar 

  • Zhang, J.-B., Gongye, Y.-Y., Chen, S.-T.: Soliton Solutions to the Coupled Gerdjikov–Ivanov Equation with Rogue-Wave-Like Phenomena. Chin. Phys. Lett. 34, 090201 (2017)

    Google Scholar 

  • Zhang, K., Han, T., Li, Z.: New single traveling wave solution of the Fokas system via complete discrimination system for polynomial method. AIMS Math. 8(1), 1925–1936 (2022)

    MathSciNet  Google Scholar 

  • Zheng, B..: New Analytical Solutions for Two Equations by a Proposed Sub-ODE Method. In: International Conference on Computer Technology and Science(ICCTS), (2012a)

  • Zheng, B.: Application of a generalized Bernoulli Sub-ODE method for finding traveling solutions of some nonlinear equations. Wseas Trans. Math. 7, 618–626 (2012b)

    Google Scholar 

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Acknowledgements

This Research is funded by Research Supporting Project Number (RSPD2023R585), King Saud University, Riyadh, Saudi Arabia.

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The authors declare that the study was realized in collaboration with equal responsibility. All authors read and approved the final manuscript.

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Correspondence to Ahmet Bekir.

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Ali, K.K., AlQahtani, S.A., Mehanna, M.S. et al. New optical soliton solutions for the (2+1) Fokas system via three techniques. Opt Quant Electron 55, 638 (2023). https://doi.org/10.1007/s11082-023-04900-y

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