Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Traveling waves for the quartic focusing Half Wave equation in one space
  dimension   We consider the quartic focusing Half Wave equation (HW) in one space
dimension. We show first that that there exist traveling wave solutions with
arbitrary small $H^{\frac 12}(\R)$ norm. This fact shows that small data
scattering is not possible for (HW) equation and that below the ground state
energy there are solutions whose energy travels as a localised packet and which
preserve this localisation in time. This behaviour for (HW) is in sharp
contrast with classical NLS in any dimension and with fractional NLS with
radial data. The second result addressed is the non existence of traveling
waves moving at the speed of light. The main ingredients of the proof are
commutator estimates and a careful study of spatial decay of traveling waves
profile using the harmonic extension to the upper half space.

19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph