Advertisement

Leapfrogging solitary waves in coupled traveling-wave field-effect transistors

  • Koichi NaraharaEmail author
Original Paper

Abstract

Leapfrogging solitary waves are characterized in two capacitively coupled traveling-wave field-effect transistors (TWFETs). The coupling implies that a nonlinear solitary wave moving on one of the devices is bounded with the wave moving on the other one, which results in the periodic amplitude/phase oscillation called leapfrogging. In conservative systems, the oscillation energy of leapfrogging is converted to the generation of radiative waves; hence, leapfrogging is shown to cease in finite duration. This study investigated the possibility of amplification of moving solitary waves to stabilize leapfrogging in coupled TWFETs. First, coupled Korteweg–de Vries equations with perturbation were derived to verify the limit-cycle dynamics of the soliton’s amplitude and phase corresponding to the stable leapfrogging. We then numerically solved the transmission equations of the coupled TWFETs to validate stable leapfrogging in practical situations.

Keywords

Leapfrogging pulses Soliton resonances Reductive perturbation Dissipative solitons Traveling-wave field-effect transistors 

Notes

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.

References

  1. 1.
    Liu, A.K., Kubota, T., Ko, D.R.S.: Resonant transfer of energy between nonlinear waves in neighboring pycnoclines. Stud. Appl. Math. 63, 26–46 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Liu, A.K., Pereira, N.R., Ko, D.R.S.: Weakly interacting internal solitary waves in neighboring pycnoclines. J. Fluid Mech. 122, 187–194 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Weidman, P.D., Johnson, M.: Experiments on leapfrogging internal solitary waves. J. Fluid Mech. 122, 195–213 (1982)CrossRefGoogle Scholar
  4. 4.
    Gear, J.A., Grimshaw, R.: Weak and strong interactions between internal solitary waves. Stud. Appl. Math. 70, 235–258 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Nitsche, M., Weidman, P.D., Grimshaw, R., Ghrist, M., Fornberg, B.: Evolution of solitary waves in a two-picnocline system. J. Fluid Mech. 642, 235–277 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kivshar, Y.S., Malomed, B.A.: Dynamics of solitons in nearly integrable systems. Rev. Mod. Phys. 61, 763–915 (1989)CrossRefGoogle Scholar
  7. 7.
    Narahara, K.: Characterization of leapfrogging solitary waves in coupled nonlinear transmission lines. Nonlinear Dyn. 81, 1805–1814 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Malomed, B.A.: Leapfrogging solitons in a system of coupled KdV equations. Wave Motion 9, 401–411 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kivshar, Y.S., Malomed, B.A.: Solitons in a system of coupled KdV equations. Wave Motion 11, 261–269 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Wright, J.D., Scheel, A.: Solitary waves and their linear stability in weakly coupled KdV equations. Z. Angew. Math. Phys. 58, 535–570 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    McIver, G.W.: A traveling-wave transistor. Proc. IEEE 53, 1747–1748 (1965)CrossRefGoogle Scholar
  12. 12.
    Holden, A.J., Daniel, D.R., Davies, I., Oxley, C.H., Rees, H.D.: Gallium arsenide traveling-wave field-effect transistors. IEEE Trans. Electron Devices 32, 61–66 (1985)CrossRefGoogle Scholar
  13. 13.
    Podgorsky, A.S., Wei, L.Y.: Theory of traveling-wave transistors. IEEE Trans. Electron Devices 29, 1845–1853 (1982)CrossRefGoogle Scholar
  14. 14.
    Narahara, K., Nakagawa, S.: Nonlinear traveling-wave field-effect transistors for amplification of short electrical pulses. IEICE Electron. Express 7, 1188–1194 (2010)CrossRefGoogle Scholar
  15. 15.
    Sardar, A., Husnine, S.M., Rizvi, S.T.R., Younis, M., Ali, K.: Multiple travelling wave solutions for electrical transmission line model. Nonlinear Dyn. 82, 1317–1324 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Salathiel, Y., Amadou, Y., Betchewe, G., Doka, S.Y., Crepin, K.T.: Soliton solutions and traveling wave solutions for a discrete electrical lattice with nonlinear dispersion through the generalized Riccati equation mapping method. Nonlinear Dyn. 87, 2435–2443 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    Akhmediev, N., Ankiewicz, A.: Dissipative Solitons. Springer, Berlin (2005)CrossRefzbMATHGoogle Scholar
  19. 19.
    Narahara, K.: Synchronization of dissipative solitons in a system of closed traveling-wave field-effect transistors. Nonlinear Dyn. 94, 711–721 (2018)CrossRefGoogle Scholar
  20. 20.
    Narahara, K.: Modulation of pulse train using leapfrogging pulses developed in unbalanced coupled nonlinear transmission lines. Math. Prob. Eng. 2018, 2869731 (2018)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Qiu, J., Sun, K., Wang, T., Gao, H.: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. (2019).  https://doi.org/10.1109/TFUZZ.2019.2895560 Google Scholar
  22. 22.
    Sun, K., Mow, S., Qiu, J., Wang, T., Gao, H.: Adaptive fuzzy control for non-triangular structural stochastic switched nonlinear systems with full state constraints. IEEE Trans. Fuzzy Syst. (2018).  https://doi.org/10.1109/TFUZZ.2018.2883374 Google Scholar
  23. 23.
    Garg, R., Bahl, I., Bozzi, M.: Microstrip Lines and Slotlines. Artech House, Boston (2013)Google Scholar
  24. 24.
    Jeffrey, A., Kawahara, T.: Asymptotic Methods in Nonlinear Wave Theory. Pitman, London (1982)zbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringKanagawa Institute of TechnologyAtsugiJapan

Personalised recommendations