Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry classification of KdV-type nonlinear evolution equations   Group classification of a class of third-order nonlinear evolution equations
generalizing KdV and mKdV equations is performed. It is shown that there are
two equations admitting simple Lie algebras of dimension three. Next, we prove
that there exist only four equations invariant with respect to Lie algebras
having nontrivial Levi factors of dimension four and six. Our analysis shows
that there are no equations invariant under algebras which are semi-direct sums
of Levi factor and radical. Making use of these results we prove that there are
three, nine, thirty-eight, fifty-two inequivalent KdV-type nonlinear evolution
equations admitting one-, two-, three-, and four-dimensional solvable Lie
algebras, respectively. Finally, we perform a complete group classification of
the most general linear third-order evolution equation.

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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat