Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real Liouvillian Extensions of Partial Differential Fields   In this paper, we establish Galois theory for partial differential systems
defined over formally real differential fields with a real closed field of
constants and over formally $p$-adic differential fields with a $p$-adically
closed field of constants. For an integrable partial differential system
defined over such a field, we prove that there exists a formally real (resp.
formally $p$-adic) Picard-Vessiot extension. Moreover, we obtain a uniqueness
result for this Picard-Vessiot extension. We give an adequate definition of the
Galois differential group and obtain a Galois fundamental theorem in this
setting. We apply the obtained Galois correspondence to characterise formally
real Liouvillian extensions of real partial differential fields with a real
closed field of constants by means of split solvable linear algebraic groups.
We present some examples of real dynamical systems and indicate some
possibilities of further development of algebraic methods in real dynamical
systems.

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The categories of this paper are: nlin
21
The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: physics
27
The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: stat