Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis
Abstract
The noiseless Burgers equation in one spatial dimension is analyzed from the point of view of a diffusive evolution equation in terms of nonlinear soliton modes and linear diffusive modes. The transient evolution of the profile is interpreted as a gas of right hand solitons connected by ramp solutions with superposed linear diffusive modes. This picture is supported by a linear stability analysis of the soliton mode. The spectrum and phase shift of the diffusive modes are determined. In the presence of the soliton the diffusive modes develop a gap in the spectrum and are phase-shifted in accordance with Levinson's theorem. The spectrum also exhibits a zero-frequency translation or Goldstone mode associated with the broken translational symmetry.
Keywords
Cite
@article{arxiv.cond-mat/9709058,
title = {Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis},
author = {Hans C. Fogedby},
journal= {arXiv preprint arXiv:cond-mat/9709058},
year = {2009}
}
Comments
9 pages, Revtex file, 5 figures, to be submitted to Phys. Rev. E