Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pattern formation with a conservation law   Pattern formation in systems with a conserved quantity is considered by
studying the appropriate amplitude equations. The conservation law leads to a
large-scale neutral mode that must be included in the asymptotic analysis for
pattern formation near onset. Near a stationary bifurcation, the usual
Ginzburg--Landau equation for the amplitude of the pattern is then coupled to
an equation for the large-scale mode. These amplitude equations show that for
certain parameters all roll-type solutions are unstable. This new instability
differs from the Eckhaus instability in that it is amplitude-driven and is
supercritical. Beyond the stability boundary, there exist stable stationary
solutions in the form of strongly modulated patterns. The envelope of these
modulations is calculated in terms of Jacobi elliptic functions and, away from
the onset of modulation, is closely approximated by a sech profile. Numerical
simulations indicate that as the modulation becomes more pronounced, the
envelope broadens. A number of applications are considered, including
convection with fixed-flux boundaries and convection in a magnetic field,
resulting in new instabilities for these systems.

25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ