Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearized Korteweg -- De Vries equation on a tree with unbounded root
  and edges   We investigate the linearized KdV equation on a metric tree consisting of
three different types of bonds: incoming unbounded root, two finite bonds, and
four outgoing unbounded bonds. Under natural assumptions at the vertices, we
obtain the uniqueness of a solution. To show the existence we use the theory of
potentials and reduce the problem to a system of linear algebraic equations. We
show that the latter is uniquely solvable under conditions of the uniqueness
theorem. Also, we show that the system we consider can be used to model wave
propagation in pipelines.

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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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: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: q-fin