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Dynamical analysis of optical soliton structures for wave propagation in nonlinear low-pass electrical transmission lines under effective approach

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Abstract

In this research work, we extracted the variety of newly optical soliton solutions which describe the wave propagation in nonlinear low-pass electrical transmission lines model by utilizing the auxiliary equation method. The secured solitons solutions yield a variety of typical soliton shapes, including dark solitons, periodic singular optical solitons, combined bright and dark solitons, kink wave solitons, bright solitons, ant-kink wave solitons, and solitary waves. The physical structure of extracted soliton solutions visualized in three different graphically structures such as three-dimension, two-dimensional and contour plotting on the choices of some constant parameters by utilizing the numerical simulations. This study explored optical solitons, solitary wave solutions, exact solitons for improving the performance of nonlinear low-pass electrical transmission systems. It provides an overview of solitons, their relevance, and stability principles. It also presents the mathematical formulation of the nonlinear low-pass electrical transmission lines model and discusses its implications for signal propagation. The secured soliton solutions have many applications in engineering and science such as nonlinear optics, fiber optics, laser optics, nonlinear dynamics, ocean engineering, electronic engineering, electrical engineering, computing engineering, power engineering and several other different kinds of physical sciences. The whole study shows that the suggested method is more powerful, effective, simple, and strong for looking into different types of nonlinear models involve in nonlinear sciences and the engineering presentation field.

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References

  • Abdoulkary, S., Beda, T., Dafounamssou, O., Tafo, E.W., Mohamadou, A.: Dynamics of solitary pulses in the nonlinear low-pass electrical transmission lines through the auxiliary equation method. J. Mod. Phys. Appl 2, 69–87 (2013)

    Google Scholar 

  • Abdoulkary, S., Mohamadou, A., Beda, T., Gambo, B., Doka, S.Y., Mahamoudou, A.: Exact traveling wave solutions to the nonlinear Schrödinger equation. Appl. Math. Comput. 233, 109–115 (2014)

    MathSciNet  Google Scholar 

  • Alam, M.N., Akbar, M.A., Mohyud-Din, S.T.: A novel \((G^{^{\prime }}/G)\)-expansion method and its application to the Boussinesq equation. Chin. Phys. B 23(2), 020203 (2014)

    Article  Google Scholar 

  • Aslan, İ: Exact solutions for a local fractional DDE associated with a nonlinear transmission line. Commun. Theor. Phys. 66(3), 315 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  • Donfack, E.F., Nguenang, J.P., Nana, L.: On the traveling waves in nonlinear electrical transmission lines with intrinsic fractional-order using discrete tanh method. Chaos Solitons Fract. 131, 109486 (2020)

    Article  MathSciNet  Google Scholar 

  • El-Borai, M.M., El-Owaidy, H.M., Ahmed, H.M., Arnous, A.H.: Exact and soliton solutions to nonlinear transmission line model. Nonlinear Dyn. 87, 767–773 (2017)

    Article  Google Scholar 

  • El-Ganaini, S., Kumar, H.: A variety of new traveling and localized solitary wave solutions of a nonlinear model describing the nonlinear low-pass electrical transmission lines. Chaos Solitons Fract. 140, 110218 (2020)

    Article  MathSciNet  Google Scholar 

  • Faridi, W.A., Asjad, M.I., Jarad, F.: Non-linear soliton solutions of perturbed Chen-Lee-Liu model by \(\Phi ^{6}\)-model expansion approach. Opt. Quant. Electron. 54(10), 664 (2022)

    Article  Google Scholar 

  • Faridi, W.A., Bakar, M.A., Myrzakulova, Z., Myrzakulov, R., Akgül, A., El Din, S.M.: The formation of solitary wave solutions and their propagation for Kuralay equation. Res Phys. 52, 106774 (2023)

    Google Scholar 

  • Fatema, K., Islam, M.E., Arafat, S.Y., Akbar, M.A.: Solitons’ behavior of waves by the effect of linearity and velocity of the results of a model in magnetized plasma field. J. Ocean Eng. Sci. 6, 66 (2022)

    Google Scholar 

  • Fendzi-Donfack, E., Kenfack-Jiotsa, A.: Extended Fan’s sub-ODE technique and its application to a fractional nonlinear coupled network including multicomponents-LC blocks. Chaos Solitons Fract. 177, 114266 (2023)

    Article  MathSciNet  Google Scholar 

  • Fendzi-Donfack, E., Nguenang, J.P., Nana, L.: Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation. Eur. Phys. J. Plus 133, 1–11 (2018)

    Article  Google Scholar 

  • Fendzi-Donfack, E., Nguenang, J.P., Nana, L.: On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission line. Nonlinear Dyn. 104, 691–704 (2021)

    Article  Google Scholar 

  • Fendzi-Donfack, E., Temgoua, G.W.K., Djoufack, Z.I., Kenfack-Jiotsa, A., Nguenang, J.P., Nana, L.: Exotical solitons for an intrinsic fractional circuit using the sine-cosine method. Chaos Solitons Fract. 160, 112253 (2022a)

    Article  MathSciNet  Google Scholar 

  • Fendzi-Donfack, E., Kumar, D., Tala-Tebue, E., Nana, L., Nguenang, J.P., Kenfack-Jiotsa, A.: Construction of exotical soliton-like for a fractional nonlinear electrical circuit equation using differential–difference Jacobi elliptic functions sub-equation method. Results Phys. 32, 105086 (2022b)

    Article  Google Scholar 

  • 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(1), 35 (2023a)

    Article  Google Scholar 

  • Fendzi-Donfack, E., Baduidana, M., Fotsa-Ngaffo, F., Kenfack-Jiotsa, A.: Construction of abundant solitons in a coupled nonlinear pendulum lattice through two discrete distinct techniques. Results Phys. 52, 106783 (2023b)

    Article  Google Scholar 

  • Hosseini, K., Seadawy, A.R., Mirzazadeh, M., Eslami, M., Radmehr, S., Baleanu, D.: Multiwave, multicomplexiton, and positive multicomplexiton solutions to a (3+1)-dimensional generalized breaking soliton equation. Alex. Eng. J. 59(5), 3473–3479 (2020)

    Article  Google Scholar 

  • Ibrahim, S., Ashir, A.M., Sabawi, Y.A., Baleanu, D.: Realization of optical solitons from nonlinear Schrödinger equation using modified Sardar sub-equation technique. Opt. Quant. Electron. 55(7), 617 (2023)

    Article  Google Scholar 

  • Iqbal, M., Seadawy, A.R.: Instability of modulation wave train and disturbance of time period in slightly stable media for unstable nonlinear Schrödinger dynamical equation. Mod. Phys. Lett. B 34(supp01), 2150010 (2020)

    Article  ADS  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Lu, D.: Construction of solitary wave solutions to the nonlinear modified Kortewege–de Vries dynamical equation in unmagnetized plasma via mathematical methods. Mod. Phys. Lett. A 33(32), 1850183 (2018a)

    Article  ADS  MathSciNet  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Lu, D.: Dispersive solitary wave solutions of nonlinear further modified Korteweg–de Vries dynamical equation in an unmagnetized dusty plasma. Mod. Phys. Lett. A 33(37), 1850217 (2018b)

    Article  ADS  MathSciNet  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Lu, D.: Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions. Mod. Phys. Lett. B 33(18), 1950210 (2019a)

    Article  ADS  MathSciNet  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Lu, D., Xia, X.: Construction of bright-dark solitons and ion-acoustic solitary wave solutions of dynamical system of nonlinear wave propagation. Mod. Phys. Lett. A 34(37), 1950309 (2019b)

    Article  ADS  MathSciNet  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Khalil, O.H., Lu, D.: Propagation of long internal waves in density stratified ocean for the (2+1)-dimensional nonlinear Nizhnik–Novikov–Vesselov dynamical equation. Results Phys. 16, 102838 (2020)

    Article  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Althobaiti, S.: Mixed soliton solutions for the (2+1)-dimensional generalized breaking soliton system via new analytical mathematical method. Results Phys. 32, 105030 (2022)

    Article  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Lu, D., Zhang, Z.: Physical structure and multiple solitary wave solutions for the nonlinear Jaulent–Miodek hierarchy equation. Mod. Phys. Lett. B 66, 2341016 (2023)

    MathSciNet  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Lu, D., Zhang, Z.: Multiple optical soliton solutions for wave propagation in nonlinear low-pass electrical transmission lines under analytical approach. Opt. Quant. Electron. 56(1), 35 (2024a)

    Article  ADS  Google Scholar 

  • Iqbal, M., Lu, D., Seadawy, A.R., Ashraf, M., Albaqawi, H.S., Khan, K.A., Chou, D.: Investigation of solitons structures for nonlinear ionic currents microtubule and Mikhaillov–Novikov–Wang dynamical equations. Opt. Quant. Electron. 56(3), 361 (2024b)

    Article  Google Scholar 

  • Islam, M.E., Barman, H.K., Akbar, M.A.: Stable soliton solutions to the nonlinear low-pass electrical transmission lines and the Cahn–Allen equation. Heliyon 7(5), 66–71 (2021)

    Article  Google Scholar 

  • Islam, M.E., Hossain, M.M., Helal, K.M., Basak, U.S., Bhowmik, R.C., Akbar, M.A.: Solitary wave analysis of the Kadomtsev–Petviashvili model in mathematical physics. Arab J. Basic Appl. Sci. 30(1), 329–340 (2023)

    Article  Google Scholar 

  • Kayum, M.A., Ara, S., Barman, H.K., Akbar, M.A.: Soliton solutions to voltage analysis in nonlinear electrical transmission lines and electric signals in telegraph lines. Results Phys. 18, 103269 (2020)

    Article  Google Scholar 

  • Kengne, E., Malomed, B.A., Chui, S.T., Liu, W.M.: Solitary signals in electrical nonlinear transmission line. J. Math. Phys. 48(1), 56–89 (2007)

    Article  MathSciNet  Google Scholar 

  • Khan, Y., Sayevand, K., Fardi, M., Ghasemi, M.: A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equations. Appl. Math. Comput. 249, 229–236 (2014)

    MathSciNet  Google Scholar 

  • Kumar, H., El-Ganaini, S.: Traveling and localized solitary wave solutions of the nonlinear electrical transmission line model equation. Eur. Phys. J. Plus 135(9), 1–25 (2020)

    Article  Google Scholar 

  • Kumar, D., Seadawy, A.R., Haque, M.R.: Multiple soliton solutions of the nonlinear partial differential equations describing the wave propagation in nonlinear low-pass electrical transmission lines. Chaos Solitons Fract. 115, 62–76 (2018a)

    Article  ADS  MathSciNet  Google Scholar 

  • Kumar, D., Seadawy, A.R., Chowdhury, R.: On new complex soliton structures of the nonlinear partial differential equation describing the pulse narrowing nonlinear transmission lines. Opt. Quant. Electron. 50, 1–14 (2018b)

    Article  Google Scholar 

  • Lu, D., Seadawy, A.R., Iqbal, M.: Mathematical methods via construction of traveling and solitary wave solutions of three coupled system of nonlinear partial differential equations and their applications. Results Phys. 11, 1161–1171 (2018)

    Article  ADS  Google Scholar 

  • Malwe, B.H., Betchewe, G., Doka, S.Y., Kofane, T.C.: Travelling wave solutions and soliton solutions for the nonlinear transmission line using the generalized Riccati equation mapping method. Nonlinear Dyn. 84, 171–177 (2016)

    Article  MathSciNet  Google Scholar 

  • Mostafa, S.I.: Analytical study for the ability of nonlinear transmission lines to generate solitons. Chaos Solitons Fract. 39(5), 2125–2132 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  • Pelap, F.B., Faye, M.M.: Solitonlike excitations in a one-dimensional electrical transmission line. J. Math. Phys. 46(3), 24–54 (2005)

    Article  MathSciNet  Google Scholar 

  • Seadawy, A.R., Iqbal, M.: Propagation of the nonlinear damped Korteweg–de Vries equation in an unmagnetized collisional dusty plasma via analytical mathematical methods. Math. Methods Appl. Sci. 44(1), 737–748 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  • Seadawy, A.R., Iqbal, M.: Dispersive propagation of optical solitions and solitary wave solutions of Kundu–Eckhaus dynamical equation via modified mathematical method. Appl. Math. A J. Chin. Univ. 38(1), 16–26 (2023)

    Article  MathSciNet  Google Scholar 

  • Seadawy, A.R., Iqbal, M., Lu, D.: Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width dynamical equation. Comput. Math. Appl. 78(11), 3620–3632 (2019)

    Article  MathSciNet  Google Scholar 

  • Seadawy, A.R., Iqbal, M., Lu, D.: Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma. Phys. A 544, 123560 (2020a)

    Article  Google Scholar 

  • Seadawy, A.R., Iqbal, M., Baleanu, D.: Construction of traveling and solitary wave solutions for wave propagation in nonlinear low-pass electrical transmission lines. J. King Saud Univ. Sci. 32(6), 2752–2761 (2020b)

    Article  Google Scholar 

  • Seadawy, A.R., Iqbal, M., Althobaiti, S., Sayed, S.: Wave propagation for the nonlinear modified Kortewege–de Vries Zakharov–Kuznetsov and extended Zakharov–Kuznetsov dynamical equations arising in nonlinear wave media. Opt. Quant. Electron. 53, 1–20 (2021)

    Article  Google Scholar 

  • Seadawy, A.R., Zahed, H., Iqbal, M.: Solitary wave solutions for the higher dimensional Jimo–Miwa dynamical equation via new mathematical techniques. Mathematics 10(7), 1011 (2022)

    Article  Google Scholar 

  • Sekulic, D.L., Sataric, M.V., Zivanov, M.B., Bajic, J.S.: Soliton-like pulses along electrical nonlinear transmission line. Elektronika ir Elektrotechnika 121(5), 53–58 (2012)

    Article  Google Scholar 

  • Wang, K.J.: Resonant multiple wave, periodic wave and interaction solutions of the new extended (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Nonlinear Dyn. 111(17), 16427–16439 (2023a)

    Article  Google Scholar 

  • Wang, K.J.: Soliton molecules, interaction and other wave solutions of the new (3+1)-dimensional integrable fourth-order equation for shallow water waves. Phys. Scr. 99(1), 015223 (2023b)

    Article  ADS  Google Scholar 

  • Wang, K.J.: Soliton molecules and other diverse wave solutions of the (2+1)-dimensional Boussinesq equation for the shallow water. Eur. Phys. J. Plus 138(10), 891 (2023c)

    Article  Google Scholar 

  • Wang, K.J.: Dynamics of complexiton, Y-type soliton and interaction solutions to the (3+1)-dimensional Kudryashov–Sinelshchikov equation in liquid with gas bubbles. Results Phys. 54, 107068 (2023d)

    Article  Google Scholar 

  • Wang, K.J., Xu, P., Shi, F.: Nonlinear dynamic behaviors of the fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation. Fractals 31(07), 2350088 (2023)

    Article  ADS  Google Scholar 

  • Wang, K.J., Hou, Q.H., Wu, H.B., Cheng, Y.Y.: Soliton molecules, novel hybrid interaction solutions and periodic wave solutions to the (3+1)-dimensional nonlinear evolution equation for shallow-water waves. Results Phys. 56, 107208 (2024)

    Article  Google Scholar 

  • Yiasir Arafat, S.M., Fatema, K., Rayhanul Islam, S.M., Islam, M.E., Ali Akbar, M., Osman, M.S.: The mathematical and wave profile analysis of the Maccari system in nonlinear physical phenomena. Opt. Quant. Electron. 55(2), 136 (2023)

    Article  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the Deanship of Graduate Studies and Scientific Research, Taif University for funding this work.

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Authors and Affiliations

  1. School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Mujahid Iqbal

  2. Department of Mathematics, University of Management and Technology, Lahore, Pakistan

    Waqas Ali Faridi

  3. Department of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh, 11495, Saudi Arabia

    Maha Alammari

  4. Department of Mathematics, College of Science and Arts, Al-Baha University, Al-Makhwah, Saudi Arabia

    Faizah A. H. Alomari

  5. Mathematics Department, Khurmah University College, Taif University, Al Hawiyah, Saudi Arabia

    Nahaa E. Alsubaie

  6. Department of Mathematics Education, Tishk International University, Erbil-Kurdistan Region, Iraq

    Salisu Ibrahim

  7. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Aly R. Seadawy

Authors
  1. Mujahid Iqbal
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  2. Waqas Ali Faridi
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  3. Maha Alammari
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  4. Faizah A. H. Alomari
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  5. Nahaa E. Alsubaie
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  6. Salisu Ibrahim
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  7. Aly R. Seadawy
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Contributions

MI: Writing-original draft preparation, formal analysis, methodology. WAF: Revised, writing-reviewing & editing. MA: Visualization, investigation. FAHA: Simulation, reviewing & editing. NEA: Software, conceptualization, resources. SI: Acquisition, validation, revised. ARS: Data curation, supervision, analysis.

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Correspondence to Mujahid Iqbal or Aly R. Seadawy.

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Iqbal, M., Faridi, W.A., Alammari, M. et al. Dynamical analysis of optical soliton structures for wave propagation in nonlinear low-pass electrical transmission lines under effective approach. Opt Quant Electron 56, 1036 (2024). https://doi.org/10.1007/s11082-024-06664-5

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