Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the propagation of regularity for solutions of the Dispersion
  Generalized Benjamin-Ono Equation   In this paper we study some properties of propagation of regularity of
solutions of the dispersive generalized Benjamin-Ono (BO) equation. This model
defines a family of dispersive equations, that can be seen as a dispersive
interpolation between Benjamin-Ono equation and Korteweg-de Vries (KdV)
equation.
  Recently, it has been showed that solutions of the KdV equation and
Benjamin-Ono equation, satisfy the following property: if the initial data has
some prescribed regularity on the right hand side of the real line, then this
regularity is propagated with infinite speed by the flow solution.
  In this case the nonlocal term present in the dispersive generalized
Benjamin-Ono equation is more challenging that the one in BO equation. To deal
with this a new approach is needed. The new ingredient is to combine commutator
expansions into the weighted energy estimate. This allow us to obtain the
property of propagation and explicitly the smoothing effect.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int