Amplitude equations for travelling wave convection

New asymptotically exact amplitude equations are derived for a dissipative system near a Hopf bifurcation. Unlike the usual coupled complex Ginzburg-Landau equations these are valid for O(1) group velocities.

[1]  Cross.  Structure of nonlinear traveling-wave states in finite geometries. , 1988, Physical review. A, General physics.

[2]  Knobloch,et al.  Oscillatory convection in binary mixtures. , 1986, Physical review. A, General physics.

[3]  Surko,et al.  Oscillatory traveling-wave convection in a finite container. , 1987, Physical review letters.

[4]  Friedrich H. Busse,et al.  Nonlinear evolution of spatio-temporal structures in dissipative continuous systems , 1990 .

[5]  Mark J. McGuinness,et al.  Amplitude equations at the critical points of unstable dispersive physical systems , 1981, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[6]  Cross,et al.  Traveling and standing waves in binary-fluid convection in finite geometries. , 1986, Physical Review Letters.

[7]  A. Newell,et al.  Evolution of the order parameter in situations with broken rotational symmetry , 1986 .

[8]  Surko,et al.  Weakly nonlinear traveling-wave convection. , 1988, Physical review letters.

[9]  Edward A. Spiegel,et al.  Intermittency through modulational instability , 1983 .

[10]  Moore,et al.  Linear stability of experimental Soret convection. , 1988, Physical review. A, General physics.

[11]  R. Heinrichs,et al.  Traveling waves and spatial variation in the convection of a binary mixture , 1987 .

[12]  Moses,et al.  Spatially and temporally modulated traveling-wave pattern in convecting binary mixtures. , 1988, Physical review letters.

[13]  Gerhard Dangelmayr,et al.  The Physics of structure formation : theory and simulation : proceedings of an international symposium, Tübingen, Fed. Rep. of Germany, October 27-November 2, 1986 , 1987 .

[14]  P. Coullet,et al.  Large scale instability of nonlinear standing waves , 1985 .

[15]  Moses,et al.  Multistability and confined traveling-wave patterns in a convecting binary mixture. , 1987, Physical review. A, General physics.

[16]  H. Haken,et al.  Two-dimensional traveling wave patterns in nonequilibrium systems , 1989 .