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Modulational instability and peak solitary wave in a discrete nonlinear electrical transmission line described by the modified extended nonlinear Schrödinger equation

  • Guy Roger Deffo
  • Serge Bruno Yamgoue
  • Francois Beceau Pelap
Regular Article

Abstract

The present work describes the propagation of plane and peak solitary waves in a modified extended nonlinear Schrödinger (MENLS) equation that was earlier shown to govern the dynamics of modulated waves in a discrete nonlinear electrical transmission line (DNLETL). Firstly, the analytic expression for the modulational instability gain is found and the influence of wavenumber and wave amplitude on the gain is derived. It is predicted that they can be used to control the occurrence of modulation instability phenomenon in the network. Afterwards, using the MENLS equation, we show that this model of nonlinear electrical transmission line admits peak solitary wave for physically realistic parameters of the system. Direct numerical simulations are performed on the exact equations of the lattice and the obtained results are in very good agreement with the analytical predictions.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    T.B. Benjamin, J. Feir, J. Fluid Mech. 27, 417 (1967) ADSCrossRefGoogle Scholar
  2. 2.
    V. Zakharov, L. Ostrovsky, Physica D 238, 540 (2009) ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    V. Bespalov, V. Talanov, ZhETF Pisma Redaktsiiu 3, 471 (1966) ADSGoogle Scholar
  4. 4.
    L.A. Ostrovskii, Sov. Phys. JETP 24, 797 (1969) ADSGoogle Scholar
  5. 5.
    E. Seve, P. Tchofo Dinda, G. Millot, M. Remoissenet, J.M. Bilbault, M. Haelterman, Phys. Rev. A 54, 3519 (1996) ADSCrossRefGoogle Scholar
  6. 6.
    A. Hasegawa, Opt. Lett. 9, 288 (1984) ADSCrossRefGoogle Scholar
  7. 7.
    G. Millot, E. Seve, S. Wabnitz, M. Haelterman, JOSA B 15, 1266 (1998) ADSCrossRefGoogle Scholar
  8. 8.
    F.K. Abdullaev, S.A. Darmanyan, J. Garnier, Prog. Opt. 44, 303 (2002) ADSCrossRefGoogle Scholar
  9. 9.
    K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 1986 ADSCrossRefGoogle Scholar
  10. 10.
    R. Malendevich, L. Jankovic, G.I. Stegeman, J.S. Aitchison, Opt. Lett. 26, 1879 (2001) ADSCrossRefGoogle Scholar
  11. 11.
    H. Fang, R. Malendevich, R. Schiek, G.I. Stegeman, Opt. Lett. 25, 1786 (2000) ADSCrossRefGoogle Scholar
  12. 12.
    V.E. Zakharov, J. Appl. Mech. Tech. Phys. 9, 190 (1968) ADSCrossRefGoogle Scholar
  13. 13.
    D. Suter, T. Blasberg, Phys. Rev. A 48, 4583 (1993) ADSCrossRefGoogle Scholar
  14. 14.
    J. Gordon, R. Leite, R. Moore, S. Porto, J. Whinnery, J. Appl. Phys. 36, 3 (1965) ADSCrossRefGoogle Scholar
  15. 15.
    S. Gatz, J. Herrmann, Opt. Lett. 23, 1176 (1998) ADSCrossRefGoogle Scholar
  16. 16.
    W. Krolikowski, O. Bang, N.I. Nikolov, D. Neshev, J. Wyller, J.J. Rasmussen, D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004) ADSCrossRefGoogle Scholar
  17. 17.
    S. Akhmanov, D. Krindach, A. Migulin, A. Sukhorukov, R. Khokhlov, IEEE J. Quantum Electron. 4, 568 (1968) ADSCrossRefGoogle Scholar
  18. 18.
    A. Mohamadou, C. Latchio Tiofack, T.C. Kofané, Phys. Rev. E 82, 016601 (2010) ADSCrossRefGoogle Scholar
  19. 19.
    S. Joo, A. Messiter, W. Schultz, J. Fluid Mech. 229, 135 (1991) ADSCrossRefGoogle Scholar
  20. 20.
    C. Kharif, R.A. Kraenkel, M. Manna, R. Thomas, J. Fluid Mech. 664, 138 (2010) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    F.B. Pelap, T.C. Kofané, N. Flytzanis, M. Remoissenet, J. Phys. Soc. Jpn. 70, 2568 (2001) ADSCrossRefGoogle Scholar
  22. 22.
    F.B. Pelap, M.M. Faye, J. Math. Phys. 46, 033502 (2005) ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    E. Kengne, W. Liu, Phys. Rev. E 73, 026603 (2006) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    S.B. Yamgoué, F.B. Pelap, Phys. Lett. A 380, 2017 (2016) ADSCrossRefGoogle Scholar
  25. 25.
    D. Yemélé, F. Kenmogné, Phys. Lett. A 373, 3801 (2009) ADSCrossRefGoogle Scholar
  26. 26.
    F. Kenmogne, D. Yemélé, Phys. Rev. E 88, 043204 (2013) ADSCrossRefGoogle Scholar
  27. 27.
    W. Królikowski, O. Bang, Phys. Rev. E 63, 016610 (2000) ADSCrossRefGoogle Scholar
  28. 28.
    O. Bang, W. Krolikowski, J. Wyller, J.J. Rasmussen, Phys. Rev. E 66, 046619 (2002) ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    A. Parola, L. Salasnich, L. Reatto, Phys. Rev. A 57, R3180 (1998) ADSCrossRefGoogle Scholar
  30. 30.
    J. Wyller, W. Krolikowski, O. Bang, J.J. Rasmussen, Phys. Rev. E 66, 066615 (2002) ADSCrossRefGoogle Scholar
  31. 31.
    W. Krolikowski, O. Bang, J.J. Rasmussen, J. Wyller, Phys. Rev. E 64, 016612 (2001) ADSCrossRefGoogle Scholar
  32. 32.
    P. Ndjoko, J.-M. Bilbault, S. Binczak, T. Kofane, Phys. Rev. E 85, 011916 (2012) ADSCrossRefGoogle Scholar
  33. 33.
    D. Yemélé, P. Marquié, J.M. Bilbault, Phys. Rev. E 68, 016605 (2003) ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    F.B. Pelap, M.M. Faye, J. Phys. Soc. Jpn. 76, 074602 (2007) ADSCrossRefGoogle Scholar
  35. 35.
    A. Mohamadou, A. Kenfack-Jiotsa, T. Kofane, Chaos Soliton. Fract. 27, 914 (2006) ADSCrossRefGoogle Scholar
  36. 36.
    L. Kavitha, M. Venkatesh, S. Dhamayanthi, D. Gopi, Chin. Phys. B 22, 129401 (2013) CrossRefGoogle Scholar
  37. 37.
    J. Li, Z. Qiao, J. Math. Phys. 54, 123501 (2013) ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    F. Kenmogne, G.B. Ndombou, D. Yemélé, A. Fomethe, Chaos Soliton. Fract. 75, 263 (2015) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Guy Roger Deffo
    • 1
  • Serge Bruno Yamgoue
    • 2
  • Francois Beceau Pelap
    • 1
  1. 1.Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques (UR-2MSP), Faculté des Sciences, Université de DschangDschangCameroon
  2. 2.Department of PhysicsHigher Teacher Training College Bambili, University of BamendaBamendaCameroon

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