Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strict self-adjointness and shallow water models   We consider a class of third order equations from the point of view of strict
self-adjointness. Necessary and sufficient conditions to the investigated class
be strictly self-adjoint are obtained. Then, from a strictly self-adjoint
subclass we consider those who admits a suitable scaling transformation.
Consequently it is derived a family of equations including the
Benjamin-Bona-Mahony, Camassa-Holm and Novikov equation. By a suitable choice
of the parameters, we deduce an one-parameter family of equations unifying the
last two mentioned equations. Then, using some recent techniques for
constructing conserved vectors, we show that from the scale invariance it is
obtained as a conserved density the same quantity employed to construct one of
the well known Hamiltonians for the cited integrable equations.

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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg