Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Class of Nonsingular Exact Solutions for Laplacian Pattern
  Formation   We present a new class of exact solutions for the so-called {\it Laplacian
Growth Equation} describing the zero-surface-tension limit of a variety of 2D
pattern formation problems. Contrary to common belief, we prove that these
solutions are free of finite-time singularities (cusps) for quite general
initial conditions and may well describe real fingering instabilities. At long
times the interface consists of N separated moving Saffman-Taylor fingers, with
``stagnation points'' in between, in agreement with numerous observations. This
evolution resembles the N-soliton solution of classical integrable PDE's.

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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org