Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Amplitude equations for systems with long-range interactions   We derive amplitude equations for interface dynamics in pattern forming
systems with long-range interactions. The basic condition for the applicability
of the method developed here is that the bulk equations are linear and solvable
by integral transforms. We arrive at the interface equation via long-wave
asymptotics. As an example, we treat the Grinfeld instability, and we also give
a result for the Saffman-Taylor instability. It turns out that the long-range
interaction survives the long-wave limit and shows up in the final equation as
a nonlocal and nonlinear term, a feature that to our knowledge is not shared by
any other known long-wave equation. The form of this particular equation will
then allow us to draw conclusions regarding the universal dynamics of systems
in which nonlocal effects persist at the level of the amplitude description.

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The categories of this paper are: quant-ph
2
The categories of this paper are: math
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org