Forced Burgers Equation in an Unbounded Domain
| dc.creator | Bec, J. | |
| dc.creator | Khanin, K. | |
| dc.date | 2002-10-01 | |
| dc.date | 2003-09-18 | |
| dc.date.accessioned | 2026-07-07T05:34:20Z | |
| dc.date.available | 2026-07-07T05:34:20Z | |
| dc.description | The inviscid Burgers equation with random and spatially smooth forcing is considered in the limit when the size of the system tends to infinity. For the one-dimensional problem, it is shown both theoretically and numerically that many of the features of the space-periodic case carry over to infinite domains as intermediate time asymptotics. In particular, for large time $T$ we introduce the concept of $T$-global shocks replacing the notion of main shock which was considered earlier in the periodic case (1997, E et al., Phys. Rev. Lett. 78, 1904). In the case of spatially extended systems these objects are no anymore global. They can be defined only for a given time scale and their spatial density behaves as $ρ(T) \sim T^{-2/3}$ for large $T$. The probability density function $p(A)$ of the age $A$ of shocks behaves asymptotically as $A^{-5/3}$. We also suggest a simple statistical model for the dynamics and interaction of shocks and discuss an analogy with the problem of distribution of instability islands for a simple first-order stochastic differential equation. | |
| dc.description | 9 pages, 10 figures, revtex4, J. Stat. Phys, in press | |
| dc.identifier | https://arxiv.org/abs/nlin/0210001 | |
| dc.identifier | http://arxiv.org/abs/nlin/0210001 | |
| dc.identifier | J. Stat. Phys. 113, 741–759 (2003) | |
| dc.identifier | doi:10.1023/A:1027356518273 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80328 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Forced Burgers Equation in an Unbounded Domain | |
| dc.type | text |