Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of a Variational Principle for PDEs with Symmetries and
  Current Conservation   We prove that under certain assumptions a partial differential equation can
be derived from a variational principle. It is well-known from Noether's
theorem that symmetries of a variational functional lead to conservation laws
of the corresponding Euler-Lagrange equation. We reverse this statement and
prove that a differential equation which satisfies sufficiently many symmetries
and corresponding conservation laws leads to a variational functional whose
Euler-Lagrange equation is the given differential equation.

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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: comp-gas