  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.

Statistical Mechanics;Chaotic Dynamics;Soft Condensed Matter;Chaotic Dynamics