SOLITONS AND DIFFUSIVE MODES IN THE NOISELESS BURGERS-EQUATION - STABILITY ANALYSIS

The noiseless Burgers equation in one spatial dimension is analyzed fr om the point of view of a diffusive evolution equation in terms. of no nlinear soliton modes and linear diffusive modes. The transient evolut ion of the profile is interpreted as a gas of right hand solitons conn ected by ramp solutions with superposed linear diffusive modes. This p icture 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 th e spectrum, and are phase shifted in accordance with Levinson's theore m. The spectrum also exhibits a zero-frequency translation or Goldston e mode associated with the broken translational symmetry.