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High-stochastic solitons for the eighth-order NLSE through Itô calculus and STD with higher polynomial nonlinearity and multiplicative white noise

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Abstract

This research is the first to deal with high stochastic solitons of the eighth-order NLSE that have higher polynomial nonlinearity and use Itô multiplicative white noise. We use each of an extended simplest approach, the addendum Kudryashov’s technique to achieve this. The examination of this study provides bright, singular, bright-singular and combined bright-dark solitons. These findings contribute to the advancement of our understanding of high stochastic solitons and their dynamics, which is crucial for real-world applications, particularly in optical communication systems. By comprehending the effects of stochasticity on dispersive solitons, we can enhance the design and performance of optical networks, leading to more efficient and reliable communication over long distances. Representations of the bright and combined bright-dark solutions are available in 2D and 3D. The system being studied is new and special, as are the effects that are discussed in the paper.

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Data Availibility Statement

All data generated or analyzed during this study are included in this manuscript.

References

  • Abdelrahman, M.A.E., Mohammed, W.W., Alesemi, M., Albosaily, S.: The effect of multiplicative noise on the exact solutions of nonlinear Schrodinger equation. AIMS Math. 6, 2970–2980 (2021)

    MathSciNet  MATH  Google Scholar 

  • Ahmed, S., Seadawy, A.R., Rizvi, S.T.R., Hameed, M.: Multi-peak and rational soliton propagations for (3+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup Kupershmidt model in fluid mechanics, ocean dynamics and plasma physics. Int. J. Geomet. Methods Mod. Phys. 20, 2350158 (2023)

    ADS  MathSciNet  Google Scholar 

  • Albosaily, S., Mohammed, W.W., Aiyashi, M.A., Abdelrahman, A.A.E.: Exact solutions of the (2+1)-dimensional stochastic chiral nonlinear Schrödinger equation. Symmetry. 12, 1874–1886 (2020)

    ADS  Google Scholar 

  • AlQahtani, S.A., Alngar, M.E.M., Shohib, R.M.A., Pathak, P.: Highly dispersive embedded solitons with quadratic \(\chi ^{(2)}\)and cubic \( \chi ^{(3)}\)non-linear susceptibilities having multiplicative white noise via Itô calculus. Chaos, Solitons and Fractals 171, 113498 (2023)

    Google Scholar 

  • Arnous, A.H., Mirzazadeh, M., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Soliton solutions to resonant nonlinear schrodinger’s equation with time-dependent coefficients by modified simple equation method. Optik 127, 11450–11459 (2016)

    ADS  Google Scholar 

  • Batool, T., Seadawy, A.R., Rizvi, S.T.R., Naqvi, S.K.: Optical multi-wave, M-shaped rational solution, homoclinic breather, periodic cross-kink and various rational solutions with interactions for Radhakrishnan-Kundu-Lakshmanan dynamical model. J. Nonlinear Opt. Phys. Mater. 32(2), 2350015 (2023)

    ADS  Google Scholar 

  • Bilige, S., Chaolu, T.: An extended simplest equation method and its application to several forms of the fifth-order KdV equation. Appl. Math. Comput. 216, 31463153 (2010)

    MathSciNet  MATH  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with Kerr law nonlinearity by F-expansion. Optik 181, 1028–1038 (2019)

    ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with quadratic-cubic law by F-expansion. Optik. 182, 930–943 (2019)

    ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with non-local nonlinearity by F-expansion. Optik. 183, 1140–1150 (2019)

    ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with kerr law nonlinearity by extended Jacobi’s elliptic function expansion. Optik 183, 395–400 (2019)

    ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with Kerr law nonlinearity by exp-function. Optik 185, 121–125 (2019)

    ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with cubic-quintic-septic law by F-expansion. Optik 182, 897–906 (2019)

    ADS  Google Scholar 

  • Biswas, A., Sonmezoglu, A., Ekici, M., Alshomrani, A.S., Belic, M.R.: Highly dispersive singular optical solitons with kerr law nonlinearity by Jacobi’s elliptic ds function expansion. Optik 192, 162954 (2019)

    ADS  Google Scholar 

  • Biswas, A., Sonmezoglu, A., Ekici, M., Alshomrani, A.S.: Highly dispersive singular optical solitons having kerr law nonlinearity by Jacobi’s elliptic cs function expansion. Optik 192, 162931 (2019)

    ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with cubic-quintic-septic law by extended Jacobi’s elliptic function expansion. Optik 183, 571–578 (2019)

    ADS  Google Scholar 

  • Biswas, A., Guzman, J.V., Mahmood, M.F., Khan, S., Ekici, M., Zhou, Q., Moshokoa, S.P., Belic, M.R.: Highly dispersive optical solitons with undetermined coefficients. Optik. 182, 890–896 (2019)

    ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with non-local nonlinearity by exp-function. Optik. 186, 288–292 (2019)

    ADS  Google Scholar 

  • Gaxiola, O., Biswas, A., Yıldırım, Y., Moraru, L.: Highly Dispersive Optical Solitons in Birefringent Fibers with Polynomial Law of Nonlinear Refractive Index by Laplace-Adomian Decomposition. Mathematics. 10, 1589 (2022)

    Google Scholar 

  • Jawad, A.J.M., Mirzazadeh, M., Zhou, Q., Biswas, A.: Optical solitons with anti-cubic nonlinearity using three integration schemes. Superlatti. Microstruct. 105, 1–10 (2017)

    ADS  Google Scholar 

  • Khan, S.: Stochastic perturbation of sub-pico second envelope solitons for Triki-Biswas equation with multi-photon absorption and bandpass lters. Optik. 183, 174–178 (2019)

    ADS  Google Scholar 

  • Khan, S.: Stochastic perturbation of optical solitons having generalized anti-cubic nonlinearity with bandpass lters and multi-photon absorption. Optik. 200, 163405 (2020)

    ADS  Google Scholar 

  • Khan, S.: Stochastic perturbation of optical solitons with quadratic-cubic nonlinear refractive index. Optik. 212, 164706 (2021)

    ADS  Google Scholar 

  • Kudryashov, N.A.: Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation. Optik. 206, 164335 (2020)

    ADS  Google Scholar 

  • Kudryashov, N.A.: Construction of nonlinear differential equations for description of propagation pulses in optical fiber. Optik 192, 162964 (2019)

    ADS  Google Scholar 

  • Kudryashov, N.A.: A generalized model for description of propagation pulses in optical fiber. Optik 189, 42–52 (2019)

    ADS  Google Scholar 

  • Kudryashov, N.A.: Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations. Appl. Math. Comput. 371, 124972 (2020)

    MathSciNet  MATH  Google Scholar 

  • Kudryashov, N.A.: Mathematical model of propagation pulse in optical fiber with power nonlinearities. Optik 212, 164750 (2020)

    ADS  Google Scholar 

  • Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equations. Optik 206, 163550 (2020)

    ADS  Google Scholar 

  • Kudryashov, N.A.: Solitary wave solutions of hierarchy with non-local nonlinearity. Appl. Math. Lett. 103, 106155 (2020)

    MathSciNet  MATH  Google Scholar 

  • Kudryashov, N.A., Antonova, E.V.: Solitary waves of equation for propagation pulse with power nonlinearities. Optik 217, 164881 (2020)

    ADS  Google Scholar 

  • Mohammed, W. W., Ahmad, H., Boulares, H., Kheli, F., El-Morshedy, M.: Exact solutions of Hirota Maccari system forced by multiplicative noise in the Itô sense. J. Low Freq. Noise, Vib. Active Control. (2021) https://doi.org/10.1177/14613484211028100

  • Mohammed, W.W., El-Morshedy, M.: The influence of multiplicative noise on the stochastic exact solutions of the Nizhnik-Novikov-Veselov system. Math. Comput. Simul. 190, 192–202 (2021)

    MathSciNet  MATH  Google Scholar 

  • Mohammed, W.W., Ahmad, H., Hamza, A.E., Aly, E.S., El-Morshedy, M., Elabbasy, E.M.: The exact solutions of the stochastic Ginzburg-Landau equation. Res. Phys. 23, 103988 (2021)

    Google Scholar 

  • Mohammed, W.W., Iqbal, N., Ali, A., El-Morshedy, M.: Exact solutions of the stochastic new coupled Konno-Oono equation. Res. Phys. 21, 103830 (2021)

    Google Scholar 

  • Mohammed, W.W., Albosaily, S., Iqbal, N., El-Morshedy, M.: The effect of multiplicative noise on the exact solutions of the stochastic Burger equation. Waves Rand. Compl. Media. (2021). https://doi.org/10.1080/17455030.2021.1905914

    Article  Google Scholar 

  • Raza, N., Javid, A.: Dynamics of optical solitons with Radhakrishnan-Kundu-Lakshmanan model via two reliable integration schemes. Optik 178, 557–566 (2019)

    ADS  Google Scholar 

  • Raza, N., Zubair, A.: Optical dark and singular solitons of generalized nonlinear Schrödinger’s equation with anti-cubic law of nonlinearity. Mod. Phys. Lett. B 33, 1950158 (2019)

    ADS  Google Scholar 

  • Raza, N., Murtaza, I.G., Sial, S., Younis, M.: On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients. Waves Rand. Compl. Media 28, 553–569 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  • Raza, N., Seadawy, A.R., Kaplan, M., Butt, A.R.: Symbolic computation and sensitivity analysis of nonlinear Kudryashov’s dynamical equation with applications. Phys. Scr 96, 105216 (2021)

    ADS  Google Scholar 

  • Rehman, H.U., Awan, A.U., Allahyani, S.A., ElDin, E.M., Binyamin, M.A., Yasin, S.: Exact solution of paraxial wave dynamical model with Kerr Media by using \(\phi ^{6}-\)model expansion technique. Res. Phys. 42, 105975 (2022)

    Google Scholar 

  • Rehman, H.U., Jafar, S., Javed, A., Hussain, S., Tahir, M.: New optical solitons of Biswas-Arshed equation using different techniques. Optik 206, 163670 (2020)

    ADS  Google Scholar 

  • Rehman, H.U., Iqbal, I., Hashemi, M.S., Mirzazadeh, M., Eslami, M.: Analysis of cubic-quartic-nonlinear Schrödinger’s equation with cubic-quintic-septic-nonic form of self-phase modulation through different techniques. Optik 287, 171028 (2023)

    ADS  Google Scholar 

  • Rehman, H.U., Awan, A.U., Eldin, S.M., Iqbal, I.: Study of optical stochastic solitons of Biswas-Arshed equation with multiplicative noise. Math 8, 21606–21621 (2023)

    MathSciNet  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Nimra, A.: Study of lump, rogue, multi, M shaped, periodic cross kink, breather lump, kink-cross rational waves and other interactions to the Kraenkel-Manna-Merle system in a saturated ferromagnetic material. Opt. Quant. Elect. 55, 813 (2023)

    Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Batool, T., Ali, K.: Several new analytical solutions for Davydov solitons in \(\alpha -\)helix proteins. Int. J. Mod. Phys. B 36(30), 2250213 (2022)

    ADS  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Farah, N., Ahmad, S.: Controlling optical soliton solutions for higher order Boussinesq equation using bilinear form. Opt. Quant. Electron. 55, 865 (2023)

    Google Scholar 

  • Seadawy, A.R., Rizvi, S.T.R., Ahmed, S., Bashir, A.: Lump solutions, Kuznetsov-Ma breathers, rogue waves and interaction solutions for magneto electro-elastic circular rod. Chaos, Solitons and Fractals 163, 112563 (2022)

    MathSciNet  MATH  Google Scholar 

  • Younas, U., Seadawy, A.R., Younis, M., Rizvi, S.T.R.: Construction of analytical wave solutions to the conformable fractional dynamical system of ion sound and Langmuir waves. Waves Rand.Compl. Media 32(6), 2587–2605 (2022)

    ADS  MathSciNet  MATH  Google Scholar 

  • Zayed, E.M.E., Shohib, R.M.A., Alngar, M.E.M., Biswas, A., Yildirim, Y., Dakova, A., Alshehri, H.M., Belic, Milivoj R.: Optical solitons with Sasa-Sastuma model having multiplicative noise via Itô calculus. Ukrain. J. Phys. Opt. 23, 9–14 (2022)

    Google Scholar 

  • Zayed, E.M.E., Shohib, R.M.A.: Optical solitons and other solutions to Biswas-Arshed equation using the extended simplest equation method. Optik 185, 626–635 (2019)

    ADS  Google Scholar 

  • Zayed, E.M.E., Gepreel, K.A., Alngar, M.E.M.: Addendum to Kudryashov’s method for finding solitons in magneto-optics waveguides to cubic-quartic NLSE with Kudryashov’s sextic power law of refractive index. Optik. 230, 166311 (2021)

    ADS  Google Scholar 

  • Zayed, E.M.E., Alngar, M.E.M., Shohib, R.M.A., Gepreel, K.A., Nofal, T.A.: Optical solitons with (2+1)-dimensional nonlinear Schrödinger equation having spatio-temporal dispersion and multiplicative white noise via Itô calculus. Optik. 261, 169204 (2022)

    ADS  Google Scholar 

  • Zubair, A., Raza, N., Mirzazadeh, M., Liu, W., Zhou, Q.: Analytic study on optical solitons in parity-time-symmetric mixed linear and nonlinear modulation lattices with non-Kerr nonlinearities. Optik 173, 249–262 (2018)

    ADS  Google Scholar 

  • Zulfiqar, H., Aashiq, A., Tariq, K.U., Ahmad, H., Almohsen, B., Aslam, M., Rehman, H.U.: On the solitonic wave structures and stability analysis of the stochastic nonlinear Schrödinger equation with the impact of multiplicative noise. Optik 289, 171250 (2023)

    ADS  Google Scholar 

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Acknowledgements

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research. (IFKSURC-1-7106).

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Authors and Affiliations

  1. New Emerging Technologies and 5 G Network and Beyond Research Chair, Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia

    Salman A. AlQahtani

  2. Basic Science Department, Higher Institute of Foreign Trade & Management Sciences, New Cairo Academy, Cario, 379, Egypt

    Reham M. A. Shohib

  3. Basic Science Department, Faculty of Computers and Artificial Intelligence, Modern University for Technology & Information, Cairo, 11585, Egypt

    Mohamed E. M. Alngar

  4. Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia

    Abdulaziz M. Alawwad

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  1. Salman A. AlQahtani
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  2. Reham M. A. Shohib
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  3. Mohamed E. M. Alngar
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  4. Abdulaziz M. Alawwad
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Correspondence to Salman A. AlQahtani or Mohamed E. M. Alngar.

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AlQahtani, S.A., Shohib, R.M.A., Alngar, M.E.M. et al. High-stochastic solitons for the eighth-order NLSE through Itô calculus and STD with higher polynomial nonlinearity and multiplicative white noise. Opt Quant Electron 55, 1227 (2023). https://doi.org/10.1007/s11082-023-05478-1

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