Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly nonlinear analysis in spatially extended systems as a formal
  perturbation scheme   The well known concept, to reduce the spatio-temporal dynamics beyond
instabilities of trivial states to amplitude modulated patterns, is reviewed
from the point of view of a formal perturbation expansion for general
dissipative partial differential equations. For codimension one instabilities
closed analytical formulas for all coefficients of the resulting amplitude
equation are given, with no further restriction on the basic equations of
motion. Both the autonomous and the explicitly time-dependent case are
discussed. For the latter, the problem of strong resonances is addressed
separately. The formal character of the expansion allows for an analysis of
higher-codimension instabilities like the Turing-Hopf instability and for the
discussion of principal limits of the amplitude approach in the present form.

22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess