Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conservation laws of partial differential equations: Symmetry, adjoint
  symmetry and nonlinear self-adjointness   Nonlinear self-adjointness method for constructing conservation laws of
partial differential equations (PDEs) is further studied. We show that any
adjoint symmetry of PDEs is a differential substitution of nonlinear
self-adjointness and vice versa. Consequently, each symmetry of PDEs
corresponds to a conservation law via a formula if the system of PDEs is
nonlinearly self-adjoint with differential substitution. As a byproduct, we
find that the set of differential substitutions includes the set of
conservation law multipliers as a subset. The results are illustrated by three
typical examples.

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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom