Steady states of the conserved Kuramoto-Sivashinsky equation
| dc.creator | Politi, Paolo | |
| dc.creator | Vaia, Ruggero | |
| dc.date | 2006-09-21 | |
| dc.date.accessioned | 2026-07-07T07:23:40Z | |
| dc.date.available | 2026-07-07T07:23:40Z | |
| dc.description | Recent work on the dynamics of a crystal surface [T.Frisch and A.Verga, Phys. Rev. Lett. 96, 166104 (2006)] has focused the attention on the conserved Kuramoto-Sivashinsky (CKS) equation: \partial_t u = -\partial_{xx}(u+u_{xx}+u_x^2), which displays coarsening. For a quantitative and qualitative understanding of the dynamics, the analysis of steady states is particularly relevant. In this paper we provide a detailed study of the stationary solutions and their explicit form is given. Periodic configurations form an increasing branch in the space wavelength-amplitude (lambda-A), with d(lambda)/dA>0. For large wavelength, lambda=4\sqrt{A} and the orbits in phase space tend to a separatrix, which is a parabola. Steady states are found up to an additive constant a, which is set by the dynamics through the conservation law \partial_t <u(x,t)>=0: a(lambda(t))=lambda^2(t)/48. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0609545 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0609545 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116064 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Materials Science | |
| dc.subject | Pattern Formation and Solitons | |
| dc.title | Steady states of the conserved Kuramoto-Sivashinsky equation | |
| dc.type | text |