Skip to main content
SpringerLink
Log in

On new complex soliton structures of the nonlinear partial differential equation describing the pulse narrowing nonlinear transmission lines

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

Abstract

The present paper studies the pulse narrowing nonlinear transmission lines equation, describing pulse narrowing in the field of communication engineering. More precisely, the pulse narrowing nonlinear transmission line equation is solved analytically using the recently developed techniques viz the modified Kudraysov method, the sine-Gordon equation expansion method and the extended sinh-Gordon equation expansion method. As a result, a wide range of dark, bright, dark–bright, singular or combined singular and optical soliton solutions for the pulse narrowing nonlinear transmission lines equation is formally obtained. All solutions have been verified back into its corresponding equation with the aid of maple package program.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Afshari, E., Hajimiri, A.: Nonlinear transmission lines for pulse shaping in silicon. IEEE J. Solid State Circuits 40(3), 744–752 (2005)

    Article  Google Scholar 

  • Baskonus, H.M.: New acoustic wave behaviors to the Davey–Stewartson equation with power law nonlinearity arising in fluid dynamics. Nonlinear Dyn. 86(1), 177–183 (2016)

    Article  MathSciNet  Google Scholar 

  • Baskonus, H.M., Bulut, H., Sulaiman, T.A.: Investigation of various travelling wave solutionsto the extended (2 + 1)-dimensional quantum ZK equation. Eur. Phys. J. Plus 132, 482 (2017)

    Article  Google Scholar 

  • Baskonus, H.M., Sulaiman, T.A., Bulut, H.: On the novel wave behaviors to the coupled nonlinear Maccaris system with complex structure. Optik 131, 1036–1043 (2017)

    Article  ADS  Google Scholar 

  • Bulut, H., Sulaiman, T.A., Baskonus, H.M.: Dark, bright and other soliton solutions to the Heisenberg ferromagnetic spin chain equation. Superlattices Microstruct. (2017a). https://doi.org/10.1016/j.spmi.2017.12.009

  • Bulut, H., Sulaiman, T.A., Baskonus, H.M.: On the new soliton and optical wave structures to some nonlinear evolution equations. Eur. Phys. J. Plus 132, 459 (2017b)

    Article  Google Scholar 

  • Bulut, H., Sulaiman, T.A., Baskonus, H.M., Akturk, T.: Complex acoustic gravity wave behaviors to some mathematical models arising in fluid dynamics and nonlinear dispersive media. Opt. Quant Electron. 50, 19 (2018)

    Article  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(2), 767–773 (2017)

    Article  Google Scholar 

  • Hosseini, K., Bekir, A., Kaplan, M.: New exact traveling wave solutions of the Tzitzica-type evolution equations arising in non-linear optics. J. Mod. Opt. 64, 1688–1692 (2017a)

    Article  ADS  Google Scholar 

  • Hosseini, K., Kumar, D., Kaplan, M., Bejarbaneh, E.Y.: New exact traveling wave solutions of the unstable nonlinear Schrdinger equations. Commun. Theor. Phys. 68(6), 761 (2017b)

    Article  ADS  Google Scholar 

  • Hosseini, K., Samadani, F., Kumar, D., Faridi, M.: New optical solitons of cubic–quartic nonlinear Schrdinger equation. Optik 157, 1101–1105 (2018)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Khater, A.H., Callebaut, D.K., Seadawy, A.R.: General soliton solutions of an n-dimensional complex Ginzburg–Landau equation. Phys. Scr. 62, 353–357 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  • Khater, A.H., Callebaut, D.K., Seadawy, A.R.: Nonlinear dispersive Kelvin–Helmholtz instabilities in magnetohydrodynamic flows. Phys. Scr. 67, 340–349 (2003)

    Article  ADS  MATH  Google Scholar 

  • Khater, M.M.A., Seadawy, A.R., Lu, D.: Dispersive optical soliton solutions for higher order nonlinear Sasa–Satsuma equation in mono mode fibers via new auxiliary equation method. Superlattices Microstruct. 113, 346–358 (2018)

    Article  Google Scholar 

  • Kumar, D., Hosseini, K., Samadani, F.: The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzica type equations in nonlinear optics. Optik 149, 439–446 (2017)

    Article  ADS  Google Scholar 

  • Kumar, D., Seadawy, Aly R., Joardar, A.K.: Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology. Chin. J. Phys. 56(1), 75–85 (2018)

    Article  MathSciNet  Google Scholar 

  • Lu, D., Seadawy, A., Arshad, M.: Applications of extended simple equation method on unstable nonlinear Schrdinger equations. Optik 140, 136–144 (2017)

    Article  ADS  Google Scholar 

  • Lu, D., Seadawy, A.R., Arshad, M.: Brightdark solitary wave and elliptic function solutions of unstable nonlinear Schrdinger equation and their applications. Opt. Quantum Electron. 50(1), 23 (2018)

    Article  Google Scholar 

  • Ma, W.-X., Yong, X., Zhang, H.-Q.: Diversity of interaction solutions to the (2 + 1)-dimensional Ito equation. Comput. Math. Appl. (2017). https://doi.org/10.1016/j.camwa.2017.09.013

  • Ma, W.X., Fuchssteiner, B.: Explicit and exact solutions to a Kolmogorov–Petrovskii–Piskunov equation. Int. J. Non-Linear Mech. 31, 329–338 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Ma, W.-X., Lee, J.-H.: A transformed rational function method and exact solutions to the 3 + 1 dimensional Jimbo Miwa equation. Chaos Solitons Fractals 42, 1356–1363 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Ma, W.-X., Zhou, Y.: Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. J. Differ. Equ. 264(4), 2633–2659 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Ma, W.-X., Zhu, Z.: Solving the (3 + 1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm. Appl. Math. Comput. 218, 11871–11879 (2012)

    MathSciNet  MATH  Google Scholar 

  • Malwe, B.H., Betchewe, G., Doka, S.Y., Kofane, T.C.: Soliton wave solutions for the nonlinear transmission line using the Kudryashov method and the \(\frac{G^{\prime }}{G}\)-expansion method. Appl. Math. Comput. 239, 299–309 (2014)

    MathSciNet  MATH  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)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  • Seadawy, A.R.: Three-dimensional nonlinear modified Zakharov–Kuznetsov equation of ion-acoustic waves in a magnetized plasma. Comput. Math. Appl. 71, 201–212 (2016)

    Article  MathSciNet  Google Scholar 

  • Seadawy, A.: The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrodinger equation and its solutions. Optik Int. J. Light Electron Opt. 139, 31–43 (2017a)

    Article  Google Scholar 

  • Seadawy, A.: 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 (2017b)

    Article  MathSciNet  Google Scholar 

  • Seadawy, A.R., Lu, D.: Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma. Results Phys. 6, 590–593 (2016)

    Article  ADS  Google Scholar 

  • Seadawy, A.R., Arshad, M., Lu, D.: Stability analysis of new exact traveling-wave solutions of new coupled KdV and new coupled Zakharov–Kuznetsov systems. Eur. Phys. J. Plus 132, 162 (2017)

    Article  Google Scholar 

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

    Google Scholar 

  • Yan, Z., Zhang, H.: New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water. Phys. Lett. A 285(5), 355–362 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Yang, J.-Y., Ma, W.-X., Qin, Z.: Lump and lump-soliton solutions to the (2 + 1)-dimensional Ito equation. Anal. Math. Phys. (2017). https://doi.org/10.1007/s13324-017-0181-9

  • Younis, M., Ali, S.: Solitary wave and shock wave solitons to the transmission line model for nano-ionic currents along microtubules. Appl. Math. Comput. 246, 460–463 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Younis, M., Rizvi, S.T.R., Ali, S.: Analytical and soliton solutions: nonlinear model of nanobioelectronics transmission lines. Appl. Math. Comput. 265, 994–1002 (2015)

    MathSciNet  Google Scholar 

  • Zayed, E.M.E., Alurrfi, K.A.E.: A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing pulse narrowing nonlinear transmission lines. J. Partial Differ. Equ. 28, 128–138 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Zayed, E.M.E., Alurrfi, K.A.E.: The generalized projective Riccati equations method and its applications to nonlinear PDEs describing nonlinear transmission Lines. Commun. Appl. Electron. 3(4), 1–8 (2015)

    Article  Google Scholar 

  • Zhang, J., Ma, W.-X.: Mixed lump-kink solutions to the BKP equation. Comput. Math. Appl. 74, 591–596 (2017)

    Article  MathSciNet  Google Scholar 

  • Zhao, H., Ma, W.-X.: Mixed lumpkink solutions to the KP equation. Comput. Math. Appl. 74, 1399–1405 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, Japan

    Dipankar Kumar

  2. Department of Physics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, Bangladesh

    Dipankar Kumar

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

    Aly R. Seadawy

  4. Mathematics Department, Faculty of Science, Beni–Suef University, Beni Suef, Egypt

    Aly R. Seadawy

  5. Department of Natural Science, Stamford University Bangladesh, Dhaka, 1217, Bangladesh

    Raju Chowdhury

Authors
  1. Dipankar Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aly R. Seadawy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raju Chowdhury
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aly R. Seadawy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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, 108 (2018). https://doi.org/10.1007/s11082-018-1383-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-018-1383-6

Keywords

Search

Navigation