Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: More common errors in finding exact solutions of nonlinear differential
  equations. I   In the recent paper by Kudryashov [Commun. Nonlinear Sci. Numer. Simulat.,
2009, V.14, 3507-3529] seven common errors in finding exact solutions of
nonlinear differential equations were listed and discussed in detail. We
indicate two more common errors concerning the similarity (equivalence with
respect to point transformations) and linearizability of differential equations
and then discuss the first of them. Classes of generalized KdV and mKdV
equations with variable coefficients are used in order to clarify our
conclusions. We investigate admissible point transformations in classes of
generalized KdV equations, obtain the necessary and sufficient conditions of
similarity of such equations to the standard KdV and mKdV equations and carried
out the exhaustive group classification of a class of variable-coefficient KdV
equations. Then a number of recent papers on such equations are commented using
the above results. It is shown that exact solutions were constructed in these
papers only for equations which are reduced by point transformations to the
standard KdV and mKdV equations. Therefore, exact solutions of such equations
can be obtained from known solutions of the standard KdV and mKdV equations in
an easier way than by direct solving. The same statement is true for other
equations which are equivalent to well-known equations with respect to point
transformations.

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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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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: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: math