Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darboux transformations for a twisted derivation and quasideterminant
  solutions to the super KdV equation   This paper is concerned with a generalized type of Darboux transformations
defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$
where $\sigma$ is a homomorphism. Such twisted derivations include regular
derivations, difference and $q$-difference operators and superderivatives as
special cases. Remarkably, the formulae for the iteration of Darboux
transformations are identical with those in the standard case of a regular
derivation and are expressed in terms of quasideterminants. As an example, we
revisit the Darboux transformations for the Manin-Radul super KdV equation,
studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140,
(1997). The new approach we take enables us to derive a unified expression for
solution formulae in terms of quasideterminants, covering all cases at once,
rather than using several subcases. Then, by using a known relationship between
quasideterminants and superdeterminants, we obtain expressions for these
solutions as ratios of superdeterminants. This coincides with the results of
Liu and Ma\~nas in all the cases they considered but also deals with the one
subcase in which they did not obtain such an expression. Finally, we obtain
another type of quasideterminant solutions to the Main-Radul super KdV equation
constructed from its binary Darboux transformations. These can also be
expressed as ratios of superdeterminants and are a substantial generalization
of the solutions constructed using binary Darboux transformations in earlier
work on this topic.

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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga