Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and instability of traveling wave solutions to nonlinear wave
  equations   In this paper, we study the stability and instability of plane wave solutions
to semilinear systems of wave equations satisfying the null condition. We
identify a condition which allows us to prove the global nonlinear asymptotic
stability of the plane wave. The proof of global stability requires us to
analyze the geometry of the interaction between the background plane wave and
the perturbation. When this condition is not met, we are able to prove linear
instability assuming an additional genericity condition. The linear instability
is shown using a geometric optics ansatz.

14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci