Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of a minimal non-scattering solution to the mass-subcritical
  generalized Korteweg-de Vries equation   In this article, we prove existence of a non-scattering solution, which is
minimal in some sense, to the mass-subcritical generalized Korteweg-de Vries
(gKdV) equation in the scale critical ^L^r space. We construct this solution by
a concentration compactness argument. Then, key ingredients are a linear
profile decomposition result adopted to ^L^r-framework and approximation of
solutions to the gKdV equation which involves rapid linear oscillation by means
of solutions to the nonlinear Schr"odinger equation.

33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc