Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The linear stability of shock waves for the nonlinear
  Schr\"odinger-Inviscid Burgers system   We investigate the coupling between the nonlinear Schr\"odinger equation and
the inviscid Burgers equation, a system which models interactions between short
and long waves, for instance in fluids. Well-posedness for the associated
Cauchy problem remains a difficult open problem, and we tackle it here via a
linearization technique. Namely, we establish a linearized stability theorem
for the Schr\"odinger--Burgers system, when the reference solution is an
entropy--satisfying shock wave to Burgers equation. Our proof is based on
suitable energy estimates and on properties of hyperbolic equations with
discontinuous coefficients. Numerical experiments support and expand our
theoretical results.

3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg