Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solitons and diffusive modes in the noiseless Burgers equation:
  Stability analysis   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.

27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th