Physics of Wave Phenomena

, Volume 23, Issue 1, pp 21–27 | Cite as

Possibility of propagation of dissipative solitons in ac-driven superlattice

  • S. V. KryuchkovEmail author
  • E. I. Kukhar’
Nonlinear Waves in Metamaterials


The renormalization equation for nonlinear electromagnetic wave propagating in ac-driven superlattice with dissipation has been derived by averaging method. The expression for dissipative soliton potential is obtained. The values of high-frequency field amplitudes allowing for two types of dissipative soliton are found. The shape and type of such solitons are shown to be regulated by changing the high-frequency field amplitude. The chaotic behavior of electrons in superlattice is investigated by the Melnikov method.


Soliton Chaotic Behavior Wave Phenomenon Electron Subsystem Melnikov Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. Unterrainer, B.J. Keay, M.C. Wanke, S.J. Allen, D. Leonard, G. Medeiros-Ribeiro, U. Bhattacharya, and M.G.W. Rodwell, “Inverse Bloch Oscillator: Strong Terahertz-Photocurrent Resonances at the Bloch Frequency,” Phys. Rev. Lett. 76, 2973 (1996).CrossRefADSGoogle Scholar
  2. 2.
    A.A. Andronov, M.N. Drozdov, D.I. Zinchenko, A.A. Marmalyuk, I.M. Nefedov, Yu.N. Nozdrin, A.A. Padalitsa, A.V. Sosnin, A.V. Ustinov, and V.I. Shashkin, “Transport in Weak Barrier Superlattices and the Problem of the Terahertz Bloch Oscillator,” Phys.-Usp. 46, 755 (2003).CrossRefADSGoogle Scholar
  3. 3.
    P.V. Ratnikov, “Superlattice Based on Graphene on a Strip Substrate,” JETP Lett. 90, 469 (2009).CrossRefADSGoogle Scholar
  4. 4.
    M. Barbier, P. Vasilopoulos, and F.M. Peeters, “Extra Dirac Points in the Energy Spectrum for Superlattices on Single-Layer Graphene,” Phys. Rev. B. 81, 075438 (2010).CrossRefADSGoogle Scholar
  5. 5.
    D. Bolmatov and C.-Y. Mou, “Graphene-Based Modulation-Doped Superlattice Structures,” JETP. 112, 102 (2011).CrossRefADSGoogle Scholar
  6. 6.
    D.V. Zav’yalov, V.I. Konchenkov, and S.V. Kryuchkov, “Transverse Current Rectification in a Graphene-Based Superlattice,” Semiconductors. 46, 109 (2012).CrossRefADSGoogle Scholar
  7. 7.
    S.V. Kryuchkov and E.I. Kukhar’, “Influence of the Constant Electric Field on the Mutual Rectification of the Electromagnetic Waves in Graphene Superlattice,” Physica E. 46, 25 (2012).CrossRefADSGoogle Scholar
  8. 8.
    M. Killi, S. Wu, and A. Paramekanti, “Graphene: Kinks, Superlattices, Landau Levels and Magnetotransport,” Int. J. Mod. Phys. B. 26, 1242007 (2012).CrossRefADSGoogle Scholar
  9. 9.
    F. Sattari and E. Faizabadi, “Band Gap Opening Effect on the Transport Properties of Bilayer Graphene Superlattice,” Int. J. Mod. Phys. B. 27, 1350024 (2013).CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Neetu Agrawal (Garg), S. Ghosh, and M. Sharma, “Electron Optics with Dirac Fermions: Electron Transport in Monolayer and Bilayer Graphene through Magnetic Barrier and Their Superlattices,” Int. J. Mod. Phys. B. 27, 1341003 (2013).CrossRefADSGoogle Scholar
  11. 11.
    Yu.A. Romanov, J.Yu. Romanova, and L.G. Mourokh, “Semiconductor Superlattice in a Biharmonic Field: Absolute Negative Conductivity and Static Electric-Field Generation,” J. Appl. Phys. 99, 013707 (2006).CrossRefADSGoogle Scholar
  12. 12.
    T. Hyart, K.N. Alekseev, and E.V. Thuneberg, “Bloch Gain in dc-ac-Driven Semiconductor Superlattices in the Absence of Electric Domains,” Phys. Rev. B. 77, 165330 (2008).CrossRefADSGoogle Scholar
  13. 13.
    T. Hyart, N.V. Alekseeva, J. Mattas, and K.N. Alekseev, “Terahertz Bloch Oscillator with a Modulated Bias,” Phys. Rev. Lett. 102, 140405 (2009).CrossRefADSGoogle Scholar
  14. 14.
    E.M. Epshtein, “Drag of Electrons by Solitons in Semiconductor Superlattice,” Sov. Phys.-Solid State. 14(12), 2422 (1980) [in Russian].Google Scholar
  15. 15.
    F.G. Bass and A.A. Bulgakov, Kinetic and Electrodynamic Phenomena in Classical and Quantum Semiconductor Superlattices (Nova Science Publ., N.Y., 1997).Google Scholar
  16. 16.
    S.Y. Mensah, F.K.A. Allotey, and N.G. Mensah, “Excitation of Breather (Bion) in Superlattice,” Phys. Scripta. 62, 212 (2000).CrossRefADSGoogle Scholar
  17. 17.
    S.V. Kryuchkov and E.I. Kukhar’, “The Solitary Electromagnetic Waves in the Graphene Superlattice,” Physica B. 408, 188 (2013).CrossRefADSGoogle Scholar
  18. 18.
    M.S. Bigelow, N.N. Lepeshkin, and R.W. Boyd, “Superluminal and Slow Light Propagation in a Room-Temperature Solid,” Science. 301, 200 (2003).CrossRefADSGoogle Scholar
  19. 19.
    T.V. Shubina, M.M. Glazov, N.A. Gippius, A.A. Toropov, D. Lagarde, P. Disseix, J. Leymarie, B. Gil, G. Pozina, J.P. Bergman, and B. Monemar, “Delay and Distortion of Slow Light Pulses by Excitons in ZnO,” Phys. Rev. B. 84, 075202 (2011).CrossRefADSGoogle Scholar
  20. 20.
    S.V. Kryuchkov and E.V. Kaplya, “Soliton Delay Line Based on a Semiconductor Superlattice,” Tech. Phys. 48, 576 (2003).CrossRefGoogle Scholar
  21. 21.
    K. Lonngren and A. Scott, Solitons in Action (Academic Press, N.Y., 1978).zbMATHGoogle Scholar
  22. 22.
    M. Rice, A.R. Bishop, J.A. Krumhansl, and S.E. Trullinger, “Weakly Pinned Frohlich Charge-Density-Wave Condensates: A New, Nonlinear, Current-Carrying Elementary Excitation,” Phys. Rev. Lett. 36,432 (1976).CrossRefADSGoogle Scholar
  23. 23.
    M.B. Mineev and V.V. Shmidt, “Radiation from a Vortex in a Long Josephson Junction Placed in an Alternating Electromagnetic Field,” Sov. Phys.-JETP. 52,453 (1980).ADSGoogle Scholar
  24. 24.
    K.M. Leung, “Mechanical Properties of Double-sine-Gordon Solitons and the Application to Anisotropic Heisenberg Ferromagnetic Chains,” Phys. Rev. B. 27,2877 (1983).CrossRefADSGoogle Scholar
  25. 25.
    D.S.L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler, and T. Chakraborty, “Properties of Graphene: a Theoretical Perspective,” Adv. Phys. 59, 261 (2010).CrossRefADSGoogle Scholar
  26. 26.
    S.V. Kryuchkov and C.A. Popov, “On the Feasibility of Making a Soliton Filter Based on a Quantum-Well Superlattice,” Semiconductors. 30, 1130 (1996).ADSGoogle Scholar
  27. 27.
    F.G. Bass, S.V. Kryuchkov, and A.I. Shapovalov, “Effect of a Uniform RF Field on the Shape of an Electromagnetic-Wave in a Quantum Superlattice,” Semiconductors. 29, 9 (1995).ADSGoogle Scholar
  28. 28.
    M. Holthause and D.W. Hone, “AC Stark Effects and Harmonic Generation in Periodic Potentials,” Phys. Rev. B. 49, 16605 (1994).CrossRefADSGoogle Scholar
  29. 29.
    S.V. Kryuchkov and E.I. Kukhar’, “Solitary Electromagnetic Waves in a Graphene Superlattice under Influence of High-Frequency Electric Field,” Superlattices and Microstructures. 70, 70 (2014).CrossRefADSGoogle Scholar
  30. 30.
    K.N. Alekseev and F.V. Kusmartsev, “Pendulum Limit, Chaos and Phase-Locking in the Dynamics of ac-Driven Semiconductor Superlattices,” Phys. Lett. A. 305, 281 (2002).CrossRefADSzbMATHGoogle Scholar
  31. 31.
    S.V. Kryuchkov, E.I. Kukhar’, and D.V. Zav’yalov, “Chaotic Behavior of the Electrons in Graphene Superlattice,” Superlattices and Microstructures. 64,427 (2013).CrossRefADSGoogle Scholar
  32. 32.
    M. Wu, G. Chen, and S. Luo, “Generalized Sine-Gordon Equation and Dislocation Dynamics of Superlattice,” Superlattices and Microstructures. 59,163 (2013).CrossRefADSGoogle Scholar
  33. 33.
    I. Mitkov and V. Zharnitsky, “π-Kinks in the Parametrically Driven Sine-Gordon Equation and Applications,” Physica D. 123, 301 (1998).CrossRefADSzbMATHMathSciNetGoogle Scholar
  34. 34.
    V. Zharnitsky, I. Mitkov, and M. Levi, “Parametrically Forced Sine-Gordon Equation and Domain Wall Dynamics in Ferromagnets,” Phys. Rev. B. 57, 5033 (1998).CrossRefADSGoogle Scholar
  35. 35.
    Yu.S. Kivshar, N. Gronbech-Jensen, and R.D. Parmentier, “Kinks in the Presence of Rapidly Varying Perturbations,” Phys. Rev. E. 49, 4542 (1994).CrossRefADSGoogle Scholar
  36. 36.
    N.R. Quintero and A. Sanchez, “AC Driven Sine-Gordon Solitons: Dynamics and Stability,” Eur. Phys. J. B. 6, 133 (1998).CrossRefADSGoogle Scholar
  37. 37.
    V. Zharnitsky, I. Mitkov, and N. Gronbech-Jensen, “π Kinks in Strongly ac Driven Sine-Gordon Systems,” Phys. Rev. E. 58, R52(R) (1998).CrossRefADSGoogle Scholar
  38. 38.
    L.D. Landau and E.M. Lifshitz, Mechanics (Pergamon, Oxford, 1969), p. 93.Google Scholar
  39. 39.
    N.N. Bogoliubov and Y.A. Mitropolsky, Asymptotic Methods in the Theory of Non-Linear Oscillations (Gordon and Breach, N.Y., 1961).Google Scholar
  40. 40.
    N.N. Rozanov, “Dissipative Optical Solitons,” Phys.-Usp. 43, 421 (2000).CrossRefADSGoogle Scholar
  41. 41.
    A.Y. Loskutov, “Dynamical Chaos: Systems of Classical Mechanics,” Phys.-Usp. 50, 939 (2007).CrossRefADSGoogle Scholar
  42. 42.
    F.C. Moon, Chaotic Vibrations (Wiley-Interscience Publ., N.Y., 1987).zbMATHGoogle Scholar
  43. 43.
    F.C. Moon, J. Cusumano, and P.J. Holmes, “Evidence for Homoclinic Orbits as a Precursor to Chaos in a Magnetic Pendulum,” Physica D. 24, 383 (1987).CrossRefADSzbMATHMathSciNetGoogle Scholar
  44. 44.
    F.C. Moon, “Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors,” ASME J. Appl.Mech. 47, 638 (1980).CrossRefADSGoogle Scholar

Copyright information

© Allerton Press, Inc. 2015

Authors and Affiliations

  1. 1.Volgograd State Socio-Pedagogical UniversityVolgogradRussia
  2. 2.Volgograd State Technical UniversityVolgogradRussia

Personalised recommendations