Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact sharp-fronted travelling wave solutions of the Fisher-KPP equation   A family of travelling wave solutions to the Fisher-KPP equation with speeds
$c=\pm 5/\sqrt{6}$ can be expressed exactly using Weierstrass elliptic
functions. The well-known solution for $c=5/\sqrt{6}$, which decays to zero in
the far-field, is exceptional in the sense that it can be written simply in
terms of an exponential function. This solution has the property that the
phase-plane trajectory is a heteroclinic orbit beginning at a saddle point and
ends at the origin. For $c=-5/\sqrt{6}$, there is also a trajectory that begins
at the saddle point, but this solution is normally disregarded as being
unphysical as it blows up for finite $z$. We reinterpret this special
trajectory as an exact sharp-fronted travelling solution to a
\textit{Fisher-Stefan} type moving boundary problem, where the population is
receding from, instead of advancing into, an empty space. By simulating the
full moving boundary problem numerically, we demonstrate how time-dependent
solutions evolve to this exact travelling solution for large time. The
relevance of such receding travelling waves to mathematical models for cell
migration and cell proliferation is also discussed.

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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: math
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th