Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis

Details Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis

1997-09-04

arxiv.org/abs/cond-mat/9709058v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, Revtex file, 5 figures, to be submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.57.2331

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.

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