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The European Physical Journal D

, Volume 62, Issue 1, pp 39–49 | Cite as

Can non-propagating hydrodynamic solitons be forced to move?

  • L. GordilloEmail author
  • T. Sauma
  • Y. Zárate
  • I. Espinoza
  • M.G. Clerc
  • N. Mujica
Article

Abstract.

Development of technologies based on localized states depends on our ability to manipulate and control these nonlinear structures. In order to achieve this, the interactions between localized states and control tools should be well modelled and understood. We present a theoretical and experimental study for handling non-propagating hydrodynamic solitons in a vertically driven rectangular water basin, based on the inclination of the system. Experiments show that tilting the basin induces non-propagating solitons to drift towards an equilibrium position through a relaxation process. Our theoretical approach is derived from the parametrically driven damped nonlinear Schrödinger equationwhich models the system. The basin tilting effect is modelled by promoting the parameters that characterize the system, e.g. dissipation, forcing and frequency detuning, as space dependent functions. A motion law for these hydrodynamic solitons can be deduced from these assumptions. The model equation, which includes a constant speed and a linear relaxation term, nicely reproduces the motion observed experimentally.

Keywords

Soliton Tilt Angle Equilibrium Position Contact Line Homoclinic Orbit 
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.

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References

  1. 1.
    A.C. Newell, Solitons in Mathematics and Physics (Society for Industrial and Applied Mathematics, Philadelphia, 1985)Google Scholar
  2. 2.
    See, e.g., L.M. Pismen,Patterns and Interfaces in Dissipative Dynamics (Springer Series in Synergetics, Berlin Heidelberg, 2006), and references therein.Google Scholar
  3. 3.
    M. Cross, H. Greenside, Pattern Formation and Dynamics in Nonequilibrium Systems (Cambridge University Press, New York, 2009)Google Scholar
  4. 4.
    P. Coullet, Int. J. Bifur. Chaos 12, 2445 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    W. van Saarloos, P.C. Hohenberg, Phys. Rev. Lett. 64, 749 (1990)ADSCrossRefGoogle Scholar
  6. 6.
    P.D. Woods, A.R. Champneys, Physica D 129, 147 (1999)zbMATHADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    G.W. Hunt, G.J. Lord, A.R. Champneys, Comput. Methods Appl. Mech. Eng. 170, 239 (1999)zbMATHADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    M.G. Clerc, C. Falcon, Physica A 356, 48 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    U. Bortolozzo, M.G. Clerc, C. Falcon, S. Residori, R. Rojas, Phys. Rev. Lett. 96, 214501 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    O. Thual, S. Fauve, J. Phys. (Paris) 49, 1829 (1988)CrossRefGoogle Scholar
  11. 11.
    O. Thual, S. Fauve, Phys. Rev. Lett. 64, 282 (1990)ADSCrossRefGoogle Scholar
  12. 12.
    V. Hakim, Y. Pomeau, Eur. J. Mech. B S10, 137 (1991)MathSciNetGoogle Scholar
  13. 13.
    M. Clerc, P. Coullet, E. Tirapegui, Phys. Rev. Lett. 83, 3820 (1999)zbMATHADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    M. Clerc, P. Coullet, E. Tirapegui, Opt. Commun. 167, 159 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    M. Clerc, P. Coullet, E. Tirapegui, Prog. Theor. Phys. S139, 337 (2000)ADSGoogle Scholar
  16. 16.
    M. Clerc, P. Coullet, E. Tirapegui, Int. J. Bifur. Chaos 11, 591 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    M.G. Clerc, P. Encina, E. Tirapegui, Int. J. Bifur. Chaos 18, 1905 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    I.V. Barashenkov, E.V. Zemlyanaya, Phys. Rev. Lett. 83, 2568 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    J.W. Miles, J. Fluid Mech. 148, 451 (1984)zbMATHADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    W. Zhang, J. Viñal, Phys. Rev. Lett. 74, 690 (1995)ADSCrossRefGoogle Scholar
  21. 21.
    M.G. Clerc, S. Coulibaly, N. Mujica, R. Navarro, T. Sauma, Phil. Trans. R. Soc. A 367, 3213 (2009)zbMATHADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    B. Denardo, B. Galvin, A. Greenfield, A. Larraza, S. Putterman, W. Wright, Phys. Rev. Lett. 68, 1730 (1992)ADSCrossRefGoogle Scholar
  23. 23.
    J.N. Kutz, W.L. Kath, R.D. Li, P. Kumar, Opt. Lett. 18, 802 (1993)ADSCrossRefGoogle Scholar
  24. 24.
    S. Longhi, Phys. Rev. E 53, 5520 (1996)ADSCrossRefGoogle Scholar
  25. 25.
    I.V. Barashenkov, M.M. Bogdan, V.I. Korobov, Europhys. Lett. 15, 113 (1991)ADSCrossRefGoogle Scholar
  26. 26.
    M.G. Clerc, S. Coulibaly, D. Laroze, Phys. Rev. E 77, 056209 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    M.G. Clerc, S. Coulibaly, D. Laroze, Int. J. Bifur. Chaos 19, 2717 (2009)zbMATHCrossRefGoogle Scholar
  28. 28.
    M.G. Clerc, S. Coulibaly, D. Laroze, Physica D 239, 72 (2010)zbMATHADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    N.V. Alexeeva, I.B. Barashennkov, G.P. Tsironis, Phys. Rev. Lett. 84, 3053 (2000)ADSCrossRefGoogle Scholar
  30. 30.
    M.G. Clerc, S. Coulibaly, D. Laroze, Int. J. Bifur. Chaos 19, 3525 (2009)zbMATHCrossRefGoogle Scholar
  31. 31.
    E. Caboche, F. Pedaci, P. Genevet, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, L.A. Lugiato, Phys. Rev. Lett. 102, 163901 (2009)ADSCrossRefGoogle Scholar
  32. 32.
    J. Wu, R. Keolian, I. Rudnick, Phys. Rev. Lett. 52, 1421 (1984)ADSCrossRefGoogle Scholar
  33. 33.
    J.W. Miles, Proc. Roy. Soc. A 297, 459 (1967)ADSCrossRefGoogle Scholar
  34. 34.
    W. Wei, W. Xinlong, W. Junyi, W. Rongjue, Phys. Lett. A 219, 74 (1996)ADSCrossRefGoogle Scholar
  35. 35.
    G. Arfken, H. Weber, Mathematical Methods for Physicists (Elsevier Academic Press, Burlington, 2001).Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • L. Gordillo
    • 1
    Email author
  • T. Sauma
    • 1
  • Y. Zárate
    • 1
  • I. Espinoza
    • 2
  • M.G. Clerc
    • 1
  • N. Mujica
    • 1
  1. 1.Departamento de Física, FCFM, Universidad de ChileSantiagoChile
  2. 2.Departamento de Física, Pontificia Universidad Católica de ChileSantiagoChile

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