Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-uniqueness for the ab-family of equations   We study the cubic ab-family of equations, which includes both the
Fokas-Olver-Rosenau-Qiao (FORQ) and the Novikov (NE) equations. For $a\neq0$,
it is proved that there exist initial data in the Sobolev space $H^s$, $s<3/2$,
with non-unique solutions. Multiple solutions are constructed by studying the
collision of 2-peakon solutions. Furthermore, we prove the novel phenomenon
that for some members of the family, collision between 2-peakons can occur even
if the "faster" peakon is in front of the "slower" peakon.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: econ