Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial
  Differential Systems Admitting a Rich Set of Symmetries   The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and
nonlinear) partial differential systems possessing a full set of differential
operators that map any function of one independent variable into a symmetry of
the corresponding system. We demonstrate that a system has the above property
if and only if this system admits a full set of formal integrals (i.e.,
differential operators which map symmetries into integrals of the system). As a
consequence, such systems possess both direct and inverse Noether operators (in
the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these
terms for operators that map cosymmetries into symmetries and perform
transformations in the opposite direction). Systems admitting Noether operators
are not exhausted by Euler-Lagrange systems and the systems with formal
integrals. In particular, a hyperbolic system admits an inverse Noether
operator if a differential substitution maps this system into a system
possessing an inverse Noether operator.

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The categories of this paper are: hep-th
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The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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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: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph