Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of nonlinear Schro¨dinger dark solitons

Abstract We describe complex Ginzburg-Landau (CGL) traveling hole solutions as singular perturbations of nonlinear Schrodinger (NLS) dark solitons. Modulation of the free parameters of the NLS solutions leads to a dynamical system describing the CGL dynamics in the vicinity of a traveling hole solution.

[1]  C. Paré,et al.  Solitary pulses in an amplified nonlinear dispersive medium. , 1989, Optics letters.

[2]  L. Gil,et al.  Defect-mediated turbulence. , 1989 .

[3]  Olaf Stiller,et al.  Hole solutions in the 1D complex Ginzburg-Landau equation , 1995 .

[4]  Konotop,et al.  Direct perturbation theory for dark solitons. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Paul Manneville,et al.  Stability and fluctuations of a spatially periodic convective flow , 1979 .

[6]  Arjen Doelman,et al.  Breaking the hidden symmetry in the Ginzburg-Landau equation , 1996 .

[7]  Ryogo Hirota,et al.  Direct method of finding exact solutions of nonlinear evolution equations , 1976 .

[8]  M. Dubois,et al.  Spatio-temporal intermittency in a 1D convective pattern: theoretical model and experiments , 1992 .

[9]  L. Gil.  Space and time intermittency behaviour of a one-dimensional complex Ginzburg-Landau equation , 1991 .

[10]  Paul Manneville,et al.  Stability of the Bekki-Nozaki hole solutions to the one-dimensional complex Ginzburg-Landau equation , 1992 .

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

[12]  Y. Kuramoto,et al.  Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium , 1976 .

[13]  L. Kramer,et al.  From dark solitons in the defocusing nonlinear Schro¨dinger to holes in the complex Ginzburg-Landau equation , 1994, patt-sol/9409003.

[14]  Elphick,et al.  Localized structures in surface waves. , 1989, Physical review. A, General physics.

[15]  Weber,et al.  Localized hole solutions and spatiotemporal chaos in the 1D complex Ginzburg-Landau equation. , 1993, Physical review letters.

[16]  L. Gil,et al.  A form of turbulence associated with defects , 1989 .

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

[18]  Yang,et al.  Perturbation-induced dynamics of dark solitons. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

[21]  K. Nozaki,et al.  Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation , 1985 .

[22]  T. Iwamoto,et al.  Stability of phase-singular solutions to the one-dimensional complex Ginzburg-Landau equation , 1993 .

[23]  H. Sakaguchi.  Instability of the Hole Solution in the Complex Ginzburg-Landau Equation , 1991 .