Skip to main content
Log in

Multiple optical soliton solutions for wave propagation in nonlinear low-pass electrical transmission lines under analytical approach

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

The nonlinear low-pass electrical transmission line equation under investigation base on analytical approach named extended modified rational expansion method. The NLETLs equation play important role in electronic engineering and communication system included connection system of computer network, signal distribution of cable television, high speed computer data buses, truck lines of routing calls in switching centers of telephone, connection between radio transmitter and receiver and its antennas and so on. In this study, we constructed multiple solitary wave solutions included anti-kink solitons, periodic solitary waves, dark silotons, kink solitons, bright solitons, singular bright, singular dark, combined bright-dark and combined dark-bright solitons under symbolic computation. The physical phenomena of calculated solutions represent graphically in contour, two and three dimensional. The all calculation prove that our proposed approach is powerful, efficient and can also usable for the investigation of other nonlinear equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

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 

  • Alruwaili, A.D., Seadawy, A.R., Iqbal, M., Beinane, S.A.O.: Dust-acoustic solitary wave solutions for mixed nonlinearity modified Korteweg-de Vries dynamical equation via analytical mathematical methods. J. Geom. Phys. 176, 104504 (2022)

    MathSciNet  Google Scholar 

  • Aslan, I.: Exact solutions for a local fractional DDE associated with a nonlinear transmission line. Commun. Theor. Phys. 66(3), 315–320 (2016)

    ADS  MathSciNet  Google Scholar 

  • Bilige, S., Chaolu, T., Wang, X.: Application of the extended simplest equation method to the coupled Schrödinger–Boussinesq equation. Appl. Math. Comp. 224, 517–523 (2013)

    Google Scholar 

  • Çelik, Nisa, Seadawy, Aly R.: Yeşim Sağlam Özkan, Emrullah Yaşar, a model of solitary waves in a nonlinear elastic circular rod: abundant different type exact solutions and conservation laws. Chaos Solitons Fractals 143, 110486 (2021)

    Google Scholar 

  • Chen, Y., Yan, Z.: New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos Soliton. Fract. 26(2), 399–406 (2005)

    ADS  MathSciNet  Google Scholar 

  • Fan, E.: The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials. Phys. Lett. A. 375(3), 493–497 (2011)

    ADS  MathSciNet  CAS  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, 32 (2018)

    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)

    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. Quantum Electron. 55, 35 (2023)

    Google Scholar 

  • Fendzi-Donfack, E., Marcial, B., Fernande, F.N., Aurélien, K.J.: Construction of abundant solitons in a coupled nonlinear pendulum lattice through two discrete distinct techniques. Results Phys. 52, 106783 (2023)

    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, 1850183 (2018)

    ADS  MathSciNet  Google Scholar 

  • Iqbal, M., Seadawy, A.R., Lu, D.: Dispersive solitary wave solutions of nonlinear further modified Kortewege-de Vries dynamical equation in a unmagnetized dusty plasma via mathematical methods. Mod. Phys. Lett. A 33, 1850217 (2018)

    ADS  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. Modern Phys. Lett. B. 33, 1950210 (2019)

    ADS  MathSciNet  CAS  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, 1950309 (2019)

    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)

    Google Scholar 

  • Iqbal, M., Seadawy, A.R., Lu, D., Xia, X.: Construction of a weakly nonlinear dispersion solitary wave solution for the Zakharov–Kuznetsov-modified equal width dynamical equation. Indian J. Phys. 94(9), 1465–1474 (2020)

    ADS  CAS  Google Scholar 

  • Javidi, M., Golbabai, A.: Numerical studies on nonlinear Schrödinger equations by spectral collocation method with preconditioning. J. Math. Anal. Appl. 333, 1119–1127 (2007)

    MathSciNet  Google Scholar 

  • Kabir, M.M., Khajeh, A., Aghdam, E.A., Koma, A.Y.: Modified Kudryashov method for finding exact solitary wave solutions of higher-order nonlinear equations. Math. Method Appl. Sci. 34(2), 213–219 (2011)

    ADS  MathSciNet  Google Scholar 

  • Kengne, E., Lakhssassi, A.: Analytical studies of soliton pulses along two-dimensional coupled nonlinear transmission lines. Chaos Solitons Fractals 73, 191–201 (2015)

    ADS  MathSciNet  Google Scholar 

  • Kengne, E., Malomed, B.A., Chui, S.T., Liu, W.M.: Solitary signals in electrical nonlinear transmission line. J. Math. Phys. 48, 013508 (2007)

    ADS  MathSciNet  Google Scholar 

  • Kochanov, M.B., Kudryashov, N.A., Sinel’shchikov, D.I.: Non-linear waves on shallow water under an ice cover. Higher order expansions. J. App. Math. Mech. 77, 25 (2013)

    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 Fractals 115, 62–76 (2018)

    ADS  MathSciNet  Google Scholar 

  • Li, B.Q., Ma, Y.L.: New application of the \((G^{^{\prime }}/G)\)-expansion method to excite soliton structures for nonlinear equation. Z. Naturfors. Sect. A 65, 518–524 (2010)

  • Lin, Y., Liu, Y., Li, Z.: Exact solutions for pattern formation in a reaction-diffusion system. Int. J. Nonlinear Sci. Numer. Simulat. 14, 307 (2013)

    MathSciNet  CAS  Google Scholar 

  • Liu, H., Yan, F.: The bifurcation and exact travelling wave solutions for (2+1)-dimensional nonlinear models generated by the Jaulent–Miodek hierarchy. Int. J. Nonlinear Sci. Int. 11(2), 200–205 (2011)

    MathSciNet  Google Scholar 

  • Lü, X., Lin, F.: Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order. Commun. Nonlinear Sci. Numer. Simulat. 32, 241 (2016)

    ADS  MathSciNet  Google Scholar 

  • Lu, D., Seadawy, A.R., Iqbal, M.: Construction of new solitary wave solutions of generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony and simplified modified form of Camassa–Holm equations. Open Phys. 16, 896–909 (2018)

    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(1), 171–177 (2016)

    MathSciNet  Google Scholar 

  • Matinfar, M., Eslami, M., Roshandel, S.: The first integral method to study the (2+1)-dimensional Jaulent–Miodek equations. Pramana 85(4), 593–603 (2015)

    ADS  Google Scholar 

  • McLean, W.: A spectral Galerkin method for a boundary integral equation. Math. Comp. 47(176), 597–607 (1986)

    MathSciNet  Google Scholar 

  • Mohamad Jawad, A.J.A., Mirzazadeh, M., Biswas, A.: Solitary wave solutions to nonlinear evolution equations in mathematical physics. Pramana 83(4), 457–471 (2014)

    ADS  Google Scholar 

  • Pelap, F.B., Faye, M.: Soliton-like excitations in a one dimensional electrical transmission line. J. Math. Phys. 46, 033502–1 (2005)

    ADS  MathSciNet  Google Scholar 

  • Riaz, M.B., Jhangeer, A., Abualnaja, K.M., Junaid-U-Rehman, M.: Conserved quantities and traveling wave profiles to the nonlinear transmission line via Lie group analysis. Phys. Scr. 96(10), 104013 (2021)

    ADS  Google Scholar 

  • Russell, J.S.: Report on Waves. In: Report of the Four-teenth Meeting of the British association for the advancement of science, pp 311-90 (1844)

  • Seadawy, R.A.: Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Comput. Math. Appl. 67, 172–180 (2014)

    MathSciNet  Google Scholar 

  • Seadawy, R.A.: Approximation solutions of derivative nonlinear Schrodinger equation with computational applications by variational method. Eur. Phys. J. Plus 130(182), 1–10 (2015)

    Google Scholar 

  • Seadawy, R.A.: Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries–Zakharov–Kuznetsov equation in a magnetized electron-positron plasma. Phys. A Stat. Mech. Appl. 455, 44–51 (2016)

    MathSciNet  CAS  Google Scholar 

  • Seadawy, A.R.: Modulation instability analysis for the generalized derivative higher order nonlinear Schrödinger equation and its the bright and dark soliton solutions. J. Electromagn. Waves Appl. 31(14), 1353–1362 (2017)

    ADS  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, 737–748 (2021)

    ADS  MathSciNet  Google Scholar 

  • Seadawy, A.R., Lu, D., Iqbal, M.: Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir waves. Pramana 93, 10 (2019)

    ADS  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, 3620–3632 (2019)

    MathSciNet  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 Uni. Sci. 32(6), 2752–2761 (2020)

    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 (2020)

    Google Scholar 

  • Seadawy, A.R., Iqbal, M., Lu, D.: The nonlinear diffusion reaction dynamical system with quadratic and cubic nonlinearities with analytical investigations. Int. J. Mod. Phys. B 34, 2050085 (2020)

    ADS  MathSciNet  Google Scholar 

  • Seadawy, A.R., Iqbal, M., Lu, D.: Propagation of long-wave with dissipation and dispersion in nonlinear media via generalized Kadomtsive–Petviashvili modified equal width-Burgers equation. Indian J. Phys. 94, 675–687 (2020)

    ADS  CAS  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)

    Google Scholar 

  • Sekulic, D.L., Satoric, M.V., Zivanov, M.B., Bajic, J.S.: Soliton-like pulses a long electrical nonlinear transmission line. Electron Electr. Eng. 121, 53–58 (2012)

    Google Scholar 

  • Wazwaz, A.M.: The Hirota’s direct method for multiple-soliton solutions for three model equations of shallow water waves. Appl. Math. Comput. 201, 489–503 (2008)

    MathSciNet  Google Scholar 

  • Zahed, H., Seadawy, A.R., Iqbal, M.: Structure of analytical ion-acoustic solitary wave solutions for the dynamical system of nonlinear wave propagation. Open Phys. 20(1), 313–333 (2022)

    Google Scholar 

  • Zhang, S., Xia, T.C.: Further improved extended Fan sub-equation method and new exact solutions of the (2+1)-dimensional Broer–Kaup–Kupershmidt equations. Appl. Math. Comput. 182(2), 1651–1660 (2006)

    MathSciNet  Google Scholar 

  • Zhao, Y.M.: F-expansion method and its application for finding new exact solutions to the Kudryashov–Sinelshchikov equation. J. Appl. Math. 2013, 895760 (2013)

    MathSciNet  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aly R. Seadawy.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Ethical approval

I hereby declare that this manuscript is the result of my independent creation under the reviewers’ comments. Except for the quoted contents, this manuscript does not contain any research achievements that have been published or written by other individuals or groups.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Iqbal, M., Seadawy, A.R., Lu, D. et al. Multiple optical soliton solutions for wave propagation in nonlinear low-pass electrical transmission lines under analytical approach. Opt Quant Electron 56, 35 (2024). https://doi.org/10.1007/s11082-023-05611-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-05611-0

Keywords

Navigation