Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Size of data in implicit function problems and singular perturbations
  for nonlinear Schr\"odinger systems   We investigate a general question about the size and regularity of the data
and the solutions in implicit function problems with loss of regularity. First,
we give a heuristic explanation of the fact that the optimal data size found by
Ekeland and S\'er\'e with their recent non-quadratic version of the Nash-Moser
theorem can also be recovered, for a large class of nonlinear problems, with
quadratic schemes. Then we prove that this heuristic observation applies to the
singular perturbation Cauchy problem for the nonlinear Schr\"odinger system
studied by M\'etivier, Rauch, Texier, Zumbrun, Ekeland, S\'er\'e. Using a "free
flow component" decomposition and applying an abstract Nash-Moser-H\"ormander
theorem, we improve the existing results regarding both the size of the data
and the regularity of the solutions.

10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an