Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation

[1]  G. V. Chester,et al.  Solid-State Physics , 1962, Nature.

[2]  G. Iooss,et al.  Elementary stability and bifurcation theory , 1980 .

[3]  P. C. Hohenberg,et al.  Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation , 1982 .

[4]  Kazuhiro Nozaki,et al.  Exact Solutions of the Generalized Ginzburg-Landau Equation , 1984 .

[5]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[6]  Couder,et al.  Dynamical regimes of directional viscous fingering: Spatiotemporal chaos and wave propagation. , 1990, Physical review letters.

[7]  Pierre Collet,et al.  Instabilities and fronts in extended systems , 1990 .

[8]  Hidetsugu Sakaguchi,et al.  Breakdown of the Phase Dynamics , 1990 .

[9]  M. Rabinovich,et al.  The “amplitude” - “phase” turbulence transition in a Ginzburg-Landau model as a critical phenomenon , 1992 .

[10]  F. Hayot,et al.  Ordered and Turbulent Patterns in Taylor-Couette Flow , 1992 .

[11]  B. M. Fulk MATH , 1992 .

[12]  M. Lücke,et al.  Convection in binary mixtures: the role of the concentration field , 1992 .

[13]  P. C. Hohenberg,et al.  Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations , 1992 .

[14]  Alain Pumir,et al.  The Eckhaus instability for traveling waves , 1992 .

[15]  Tuckerman,et al.  Symmetry-breaking bifurcations in one-dimensional excitable media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[16]  P. Hohenberg,et al.  Phase VS. Defect Turbulence in the 1D Complex Ginzburg-Landau Equation , 1992 .

[17]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[18]  Hsueh-Chia Chang,et al.  Laminarizing effects of dispersion in an active-dissipative nonlinear medium , 1993 .

[19]  Hugues Chaté,et al.  Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation , 1993, patt-sol/9310001.

[20]  Egolf,et al.  Characterization of the transition from defect to phase turbulence. , 1994, Physical review letters.

[21]  Paul Manneville,et al.  Dissipative Structures and Weak Turbulence , 1995 .

[22]  Paul Manneville,et al.  Phase turbulence in the two-dimensional complex Ginzburg-Landau equation , 1996 .

[23]  Q. Ouyang,et al.  Transition from spirals to defect turbulence driven by a convective instability , 1996, Nature.

[24]  San Miguel M,et al.  Winding Number Instability in the Phase-Turbulence Regime of the Complex Ginzburg-Landau Equation. , 1996, Physical review letters.

[25]  Torcini Order Parameter for the Transition from Phase to Amplitude Turbulence. , 1996, Physical review letters.

[26]  Alessandro Torcini,et al.  Studies of phase turbulence in the one-dimensional complex Ginzburg-Landau equation , 1996, chao-dyn/9608003.

[27]  M. Dubois,et al.  Critical properties of convective waves in a one-dimensional system , 1997 .

[28]  Emilio Hernández-García,et al.  Wound-up phase turbulence in the complex Ginzburg-Landau equation , 1997, chao-dyn/9701023.

[29]  Robert E. Ecke,et al.  Eckhaus-Benjamin-Feir Instability in Rotating Convection , 1997 .

[30]  Jerry P. Gollub,et al.  OSCILLATIONS AND SPATIOTEMPORAL CHAOS OF ONE-DIMENSIONAL FLUID FRONTS , 1997 .

[31]  Martin van Hecke,et al.  Building Blocks of Spatiotemporal Intermittency , 1997, chao-dyn/9707010.

[32]  Hsueh-Chia Chang,et al.  Generation and Suppression of Radiation by Solitary Pulses , 1998, SIAM J. Appl. Math..

[33]  Arnaud Chiffaudel,et al.  Supercritical Eckhaus Instability for Surface-Tension-Driven Hydrothermal Waves , 1998 .

[34]  Angelo Vulpiani,et al.  Dynamical Systems Approach to Turbulence , 1998 .

[35]  S. Akamatsu,et al.  ANISOTROPY-DRIVEN DYNAMICS OF CELLULAR FRONTS IN DIRECTIONAL SOLIDIFICATION IN THIN SAMPLES , 1998 .

[36]  Javier Burguete,et al.  BEKKI-NOZAKI AMPLITUDE HOLES IN HYDROTHERMAL NONLINEAR WAVES , 1999, patt-sol/9904005.

[37]  Velarde,et al.  Internal waves excited by the marangoni effect , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  I. Mutabazi,et al.  Dynamics of spatio-temporal defects in the Taylor-Dean system , 2000 .

[39]  Giacomelli,et al.  Convective lyapunov exponents and propagation of correlations , 2000, Physical review letters.

[40]  Markus Bär,et al.  Stable bound states of pulses in an excitable medium , 2000 .

[41]  Zhou,et al.  Experimental studies on long-wavelength instability and spiral breakup in a reaction-diffusion system , 2000, Physical review letters.

[42]  Bar,et al.  Modulated amplitude waves and the transition from phase to defect chaos , 2000, Physical review letters.

[43]  Q Ouyang,et al.  Transition from spirals to defect-mediated turbulence driven by a doppler instability. , 2000, Physical review letters.

[44]  M van Hecke,et al.  Ordered and self-disordered dynamics of holes and defects in the one-dimensional complex Ginzburg-Landau equation. , 2001, Physical review letters.

[45]  I. Aranson,et al.  The world of the complex Ginzburg-Landau equation , 2001, cond-mat/0106115.