Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symbolic Computation of Conservation Laws of Nonlinear Partial
  Differential Equations in Multi-dimensions   A direct method for the computation of polynomial conservation laws of
polynomial systems of nonlinear partial differential equations (PDEs) in
multi-dimensions is presented. The method avoids advanced
differential-geometric tools. Instead, it is solely based on calculus,
variational calculus, and linear algebra.
  Densities are constructed as linear combinations of scaling homogeneous terms
with undetermined coefficients. The variational derivative (Euler operator) is
used to compute the undetermined coefficients. The homotopy operator is used to
compute the fluxes.
  The method is illustrated with nonlinear PDEs describing wave phenomena in
fluid dynamics, plasma physics, and quantum physics. For PDEs with parameters,
the method determines the conditions on the parameters so that a sequence of
conserved densities might exist. The existence of a large number of
conservation laws is a predictor for complete integrability. The method is
algorithmic, applicable to a variety of PDEs, and can be implemented in
computer algebra systems such as Mathematica, Maple, and REDUCE.

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The categories of this paper are: q-alg
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ