Skip to main content
Log in

Propagation of nonlinear waves in bi-inductance nonlinear transmission lines

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We consider a one-dimensional modified complex Ginzburg-Landau equation, which governs the dynamics of matter waves propagating in a discrete bi-inductance nonlinear transmission line containing a finite number of cells. Employing an extended Jacobi elliptic functions expansion method, we present new exact analytical solutions which describe the propagation of periodic and solitary waves in the considered network.

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.

Similar content being viewed by others

References

  1. A.C. Scott, Emergency and Dynamics of Coherent Structures, Nonlinear Science (Oxford University Press, New York, 1999)

  2. A. Hasegawa, Optical Solitons in Fibers, 2nd edn. (Springer, Berlin, 1989)

  3. M. Remoissenet, Waves Called Solitons, 3rd edn. (Springer, Berlin, 1999)

  4. N.J. Zabusky, M.D. Kruskal, Phys. Rev. Lett. 15, 240 (1965)

    Article  MATH  ADS  Google Scholar 

  5. K. Lonngren, in Solitons in Action, edited by K. Lonngren, A. Scott (Academic, New York, 1978)

  6. T. Taniuti, N. Yajima, J. Math. Phys. 10, 1369 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  7. E. Kengne, R. Vaillancourt, Can. J. Phys. 87, 1191 (2009)

    Article  ADS  Google Scholar 

  8. E. Kengne, J. Maths. Phys. 48, 013508 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  9. E. Kengne, V. Bozic, M. Viana, R. Vaillancourt, Phys. Rev. E 78, 026603 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  10. T. Kakutani, N. Yamasaki, J. Phys. Soc. Jpn 45, 674 (1978)

    Article  ADS  Google Scholar 

  11. R. Hirota, K. Suzuki, Proc. IEEE 61, 1483 (1973)

    Article  Google Scholar 

  12. A.C. Scott, Active and Nonlinear Wave Propagation in Electronics (Wiley-Interscience, New York, 1970)

  13. E. Afshari, A. Hajimiri, IEEE J. Solid-State Circuits 40, 744 (2005)

    Article  Google Scholar 

  14. E. Kengne, W.M. Liu, Phys. Rev. E 73, 026603 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  15. M. Marklund, P.K. Shukla, Phys. Rev. E 73, 057601 (2006)

    Article  ADS  Google Scholar 

  16. Z.Y. Yan, Chaos Solitons Fractals 16, 759 (2003)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. F.B. Pelap, T.C. Kofané, N. Flytzanis, M. Remoissenet, J. Phys. Soc. Jpn 70, 2568 (2001)

    Article  ADS  Google Scholar 

  18. E. Kengne, J. Nonlin. Oscillations 6, 339 (2003)

    Article  MathSciNet  Google Scholar 

  19. E.T. Whittaker, G.N. Watson, in A Course of Modern Analysis (Cambridge University Press, Cambridge, 1927), pp. 452–455

  20. H.W. Schurmann, Phys. Rev. E 54, 4312 (1996)

    Article  ADS  Google Scholar 

  21. M.J. Ablowitz, P.A. Clarkson, Soliton, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, 1991)

  22. H.W. Schürmann, V.S. Serov, J. Nickel, Int. J. Theor. Phys. 45, 1093 (2006)

    Article  MATH  Google Scholar 

  23. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Emmanuel Kengne.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kengne, E., Lakhssassi, A. Propagation of nonlinear waves in bi-inductance nonlinear transmission lines. Eur. Phys. J. B 87, 237 (2014). https://doi.org/10.1140/epjb/e2014-50406-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50406-8

Keywords

Navigation