Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical exponents line, scattering thoeries for a weighted gradient
  system of semilinear Schrodinger equations   We establish the local wellposedness of different type of solutions the
system with different types of initial data. We find there exists a critical
exponents line in space dimension 3 and critical exponents point in space
dimension 4. We also establish different scattering theories for the global
solutions.

25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat