Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry of periodic traveling waves for nonlocal dispersive equations   Of concern is the a priori symmetry of traveling wave solutions for a general
class of nonlocal dispersive equations \[ u_t +(u^2 +Lu)_x =0, \] where $L$ is
a Fourier multiplier operator with symbol $m$. Our analysis includes both
homogeneous and inhomogeneous symbols. We characterize a class of symbols $m$
guaranteeing that periodic traveling wave solutions are symmetric under a mild
assumption on the wave profile. Particularly, instead of considering waves with
a unique crest and trough per period or a monotone structure near troughs as
classically imposed in the water wave problem, we formulate a reflection
criterion, which allows to affirm the symmetry of periodic traveling waves. The
reflection criterion weakens the assumption of monotonicity between trough and
crest and enables to treat a priori solutions with multiple crests of different
sizes per period. Moreover, our result not only applies to smooth solutions,
but also to traveling waves with a non-smooth structure such as peaks or cusps
at a crest. The proof relies on a so-called touching lemma, which is related to
a strong maximum principle for elliptic operators, and a weak form of the
celebrated method of moving planes.

37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat