Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions   Quaternion-valued solutions to the non-commutative KdV equation are produced
using determinants. The solutions produced in this way are (breather) soliton
solutions, rational solutions, spatially periodic solutions and hybrids of
these three basic types. A complete characterization of the parameters that
lead to non-singular 1-soliton and periodic solutions is given. Surprisingly,
it is shown that such solutions are never singular when the solution is
essentially non-commutative. When a 1-soliton solution is combined with another
solution through an iterated Darboux transformation, the result behaves
asymptotically like a combination of different solutions. This ``non-linear
superposition principle'' is used to find a formula for the phase shift in the
general 2-soliton interaction. A concluding section compares these results with
other research on non-commutative soliton equations and lists some open
questions.

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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc