Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear Stability of Modulated Fronts for the Swift-Hohenberg
  Equation   We consider front solutions of the Swift-Hohenberg equation $\partial_t u=
-(1+\partial_x^2)^2 u +\epsilon ^2 u -u^3$. These are traveling waves which
leave in their wake a periodic pattern in the laboratory frame. Using
renormalization techniques and a decomposition into Bloch waves, we show the
non-linear stability of these solutions. It turns out that this problem is
closely related to the question of stability of the trivial solution for the
model problem $\partial_t u(x,t) = \partial_x^2 u
(x,t)+(1+\tanh(x-ct))u(x,t)+u(x,t)^p$ with $p>3$. In particular, we show that
the instability of the perturbation ahead of the front is entirely compensated
by a diffusive stabilization which sets in once the perturbation has hit the
bulk behind the front.

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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: cs