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

Hans C. Fogedby
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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.

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BibTeXRIS

Hans C. Fogedby. 1997-09-04. Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis. https://doi.org/10.1103/physreve.57.2331

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