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Traveling pulse on a periodic background in parametrically driven systems

Alejandro O. León* and Marcel G. Clerc†

Saliya Coulibaly‡

  • Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile

  • Laboratoire de Physique des Lasers, Atomes et Molécules, CNRS UMR 8523, Université des Sciences et Technologies de Lille–59655 Villeneuve d'Ascq Cedex, France, EU

  • *aoleon@dfi.uchile.cl
  • †marcel@dfi.uchile.cl
  • ‡saliya.coulibaly@univ-lille1.fr
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Phys. Rev. E 91, 050901(R) – Published 8 May, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.050901

Abstract

Macroscopic systems with dissipation and time-modulated injection of energy, parametrically driven systems, can self-organize into localized states and/or patterns. We investigate a pulse that travels over a one-dimensional pattern in parametrically driven systems. Based on a minimal prototype model, we show that the pulses emerge through a subcritical Andronov-Hopf bifurcation of the underlying pattern. We describe a simple physical system, a magnetic wire forced with a transverse oscillatory magnetic field, which displays these traveling pulses.

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References (36)

  1. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977).
  2. M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65, 851 (1993).
  3. P. Brunet, J. M. Flesselles, and L. Limat, Elastic properties of a cellular dissipative structure, Euro. Phys. J. B 35, 525 (2003).
  4. L. Pan, and J. R. de Bruyn, Spatially uniform traveling cellular patterns at a driven interface, Phys. Rev. E 49, 483 (1994).
  5. P. Coullet, R. E. Golstein, and G. H. Gunaratne, Parity-Breaking Transitions of Modulated Patterns in Hydrodynamic Systems, Phys. Rev. Lett. 63, 1954 (1989).
  6. C. Counillon, L. Daudet, T. Podgorski, and L. Limat, Dynamics of a Liquid Column Array under Periodic Boundary Conditions, Phys. Rev. Lett. 80, 2117 (1998).
  7. P. Brunet, Stabilized Kuramoto-Sivashinsky equation: A useful model for secondary instabilities and related dynamics of experimental one-dimensional cellular flows, Phys. Rev. E 76, 017204 (2007).
  8. P. Coullet and G. Iooss, Instabilitiy of One-Dimensional Cellular Patterns, Phys. Rev. Lett. 64, 866 (1990).
  9. L. Gil, Instabilities of one-dimensional cellular patterns: Far from the secondary threshold, Europhys. Lett. 48, 156 (1999).
  10. L. Gil, Secondary instability of one-dimensional cellular patterns: A gap soliton, black soliton and breather analogy, Physica D 147, 300 (2000).
  11. L. D. Landau and E. M. Lifshiftz, Mechanics, Course of Theoretical Physics Vol. 1 (Pergamon, New York, 1976).
  12. M. Faraday, On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces, Philos. Trans. R. Soc. London 121, 299 (1831).
  13. J. W. Miles, Parametrically excited solitary waves, J. Fluid Mech. 148, 451 (1984).
  14. M. G. Clerc, S. Coulibaly, N. Mujica, R. Navarro, and T. Sauma, Soliton pair interaction law in parametrically driven Newtonian fluid, Philos. Trans. R. Soc., A 367, 3213 (2009).
  15. I. V. Barashenkov, M. M. Bogdan, and V. I. Korobov, Stability diagram of the phase-locked solitons in the parametrically driven, damped nonlinear Schrödinger equation, Europhys. Lett. 15, 113 (1991).
  16. S. R. Woodford and I. V. Barashenkov, Stability of the Bloch wall via the Bogomolnyi decomposition in elliptic coordinates, J. Phys. A: Math. Theor. 41, 185203 (2008).
  17. M. G. Clerc, S. Coulibaly, and D. Laroze, Localized states of parametrically driven easy-plane ferromagnetic wire, Physica D 239, 72 (2010).
  18. M. G. Clerc, S. Coulibaly, and D. Laroze, Localized states beyond the asymptotic parametrically driven amplitude equation, Phys. Rev. E 77, 056209 (2008).
  19. B. Denardo, B. Galvin, A. Greenfield, A. Larraza, S. Putterman, and W. Wright, Observations of localized structures in nonlinear lattices: Domain walls and kinks, Phys. Rev. Lett. 68, 1730 (1992).
  20. J. N. Kutz, W. L. Kath, R.-D. Li, and P. Kumar, Long-distance pulse propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers, Opt. Lett. 18, 802 (1993).
  21. S. Longhi, Stable multipulse states in a nonlinear dispersive cavity with parametric gain, Phys. Rev. E 53, 5520 (1996).
  22. A. O. León and M. G. Clerc, Spin-transfer-driven nano-oscillators are equivalent to parametric resonators, Phys. Rev. B 91, 014411 (2015).
  23. S. Douady, S. Fauve, and C. Laroche, Subharmonic instabilities and defects in a granular layer under vertical vibrations, Europhys. Lett. 8, 621 (1989).
  24. I. Espinoza, Control de solitones disipativos en un fluido forzado paramétricamente, Pontificia Universidad Católica de Chile, 2009.
  25. A. J. Simon, J. Bechhoefer, and A. Libchaber, Solitary Modes and the Eckaus Instability in Directional Solidification, Phys. Rev. Lett. 61, 2574 (1988).
  26. M. G. Clerc, S. Coulibaly, and D. Laroze, Parametrically driven instabilities in quasi-reversal systems, Int. J. Bifurcation Chaos 19, 3525 (2009).
  27. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, New York, 1992).
  28. P. Coullet, T. Frisch, and G. Sonnino, Dispersion-induced patterns, Phys. Rev. E 49, 2087 (1994).
  29. I. D. Mayergoyz, G. Bertotti, and C. Serpico, Nonlinear Magnetization Dynamics in Nanosystems (Elsevier, Oxford, 2009).
  30. I. V. Barashenkov and E. V. Zemlyanaya, Traveling solitons in the damped-driven nonlinear Schrödinger equation, SIAM J. Appl. Math. 64, 800 (2004).
  31. I. V. Barashenkov, E. V. Zemlyanaya, and T. C. van Heerden, Time-periodic solitons in a damped-driven nonlinear Schrödinger equation, Phys. Rev. E 83, 056609 (2011).
  32. I. V. Barashenkov and E. V. Zemlyanaya, Soliton complexity in the damped-driven nonlinear Schrödinger equation: Stationary to periodic to quasiperiodic complexes, Phys. Rev. E 83, 056610 (2011).
  33. D. Urzagasti, D. Laroze, M. G. Clerc, S. Coulibaly, and H. Pleiner, Two-soliton precession state in a parametrically driven magnetic wire, J. Appl. Phys. 111, 07D111 (2012).
  34. M. G. Clerc, M. A. Garcia-Ñustes, Y. Zárate, and S. Coulibaly, Phase shielding soliton in parametrically driven systems, Phys. Rev. E 87, 052915 (2013).
  35. D. Urzagasti, D. Laroze, M. G. Clerc, H. Pleiner, Breather soliton solutions in a parametrically driven magnetic wire, Europhys. Lett. 104, 40001 (2013).
  36. M. G. Clerc, S. Coulibaly, and D. Laroze, Localized waves in a parametrically driven magnetic nanowire, Europhys. Lett. 97, 30006 (2012).

Outline

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Phys. Rev. E 91, 050901(R)– Published 8 May, 2015
  • Received 11 February 2015

©2015 American Physical Society

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