One-dimensional pattern formation with galilean invariance near a stationary bifurcation

@article{Matthews2000OnedimensionalPF,
  title={One-dimensional pattern formation with galilean invariance near a stationary bifurcation},
  author={Matthews and Cox},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={2000},
  volume={62 2 Pt A},
  pages={R1473-6}
}
  • Matthews, Cox
  • Published 2000 in
    Physical review. E, Statistical physics, plasmas…
One-dimensional pattern formation with Galilean symmetry is not governed by the Ginzburg-Landau equation near onset; an additional equation describing a large-scale mean flow is required. We derive these amplitude equations and predict the solution amplitude. All steady patterns are unstable, with the growth of the instability taking place on a faster time scale than the formation of the pattern itself. Numerical simulations show that chaotic solutions are obtained, whose amplitude is… CONTINUE READING