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Houghton, S.M.; Tobias, S.M.; Knobloch, E.; Proctor, M.R.E. (2009)
Publisher: Elsevier
Languages: English
Types: Article
Properties of the complex Ginzburg-Landau equation with drift are studied focusing on the Benjamin-Feir stable regime. On a finite interval with Neumann boundary conditions the equation exhibits bistability between a spatially uniform time-periodic state and a variety of nonuniform states with complex time dependence. The origin of this behavior is identified and contrasted with the bistable behavior present with periodic boundary conditions and no drift.
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    • [1] I. S. Aranson, L. Kramer, The world of the complex GinzburgLandau equation, Rev. Mod. Phys. 74 (2002) 99-143.
    • [2] L. Brusch, M. G. Zimmermann, M. van Hecke, M. Ba¨r, A. Torcini, Modulated amplitude waves and the transition from phase to defect chaos, Phys. Rev. Lett. 85 (2000) 86-89.
    • [3] J. R. Cash, D. R. Moore, A high order method for the numerical solution of two-point boundary value problems, BIT Numerical Mathematics 20 (1980) 44-52.
    • [4] H. Chat´e, Spatiotemporal intermittency regimes of the onedimensional complex Ginzburg-Landau equation, Nonlinearity 7 (1994) 185-204.
    • [5] S. J. Cowley, F. T. Smith, On the stability of Poiseuille-Couette flow: a bifurcation from infinity, J. Fluid Mech. 156 (1985) 83- 100.
    • [6] M. C. Cross, P. C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65 (1993) 851-1112.
    • [7] R. J. Deissler, Noise-sustained structure, intermittency, and the Ginzburg-Landau equation, J. Stat. Phys. 40 (1985) 371-395.
    • [8] B. Eckhardt, T. M. Schneider, B. Hof, J.Westerweel, Turbulence transition in pipe flow, Ann. Rev. Fluid Mech. 39 (2007) 447- 468.
    • [9] M. Golubitsky, D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. I, New York: Springer, 1985.
    • [10] J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, New York: Springer, 1984.
    • [11] R. R. Kerswell, Recent progress in understanding the transition to turbulence in a pipe, Nonlinearity 18 (2005) R17-R44.
    • [12] M. R. E. Proctor, S. M. Tobias, E. Knobloch, Noise-sustained structures due to convective instability in finite domains, Phys. D 145 (2000) 191-206.
    • [13] S. Rosenblat, S. H. Davis, Bifurcation from infinity, SIAM J. Appl. Math. 37 (1979) 1-19.
    • [14] F. Schilder, H. M. Osinga, W. Vogt, Continuation of quasiperiodic invariant tori, SIAM J. App. Dyn. Sys. 4 No. 3 (2005) 459-488.
    • [15] F. Schilder, W. Vogt, S. Schreiber, H. M. Osinga, Fourier methods for quasi-periodic oscillations, Int. J. Numer. Meth. Engng. 67 (2006) 629-671.
    • [16] K. Stewartson, J. T. Stuart, A non-linear instability theory for a wave system in plane Poiseuille flow, J. Fluid Mech. 48 (1971) 529-545.
    • [17] S. M. Tobias, E. Knobloch, Breakup of spiral waves into chemical turbulence, Phys. Rev. Lett. 80 (1998) 4811-4814.
    • [18] S. M. Tobias, M. R. E. Proctor, E. Knobloch, The role of absolute instability in the solar dynamo, Astron. Astrophys. 318 (1997) L55-L58.
    • [19] S. M. Tobias, M. R. E. Proctor, E. Knobloch, Convective and absolute instabilities of fluid flows in finite geometry, Phys. D 113 (1998) 43-72.
    • [20] M. van Hecke, Building blocks of spatiotemporal intermittency, Phys. Rev. Lett. 80 (1998) 1896-1899.
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