Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conservation laws, symmetries, and line soliton solutions of generalized
  KP and Boussinesq equations with p-power nonlinearities in two dimensions   Nonlinear generalizations of integrable equations in one dimension, such as
the KdV and Boussinesq equations with $p$-power nonlinearities, arise in many
physical applications and are interesting in analysis due to critical
behaviour. This paper studies analogous nonlinear $p$-power generalizations of
the integrable KP equation and the Boussinesq equation in two dimensions.
Several results are obtained. First, for all $p\neq 0$, a Hamiltonian
formulation of both generalized equations is given. Second, all Lie symmetries
are derived, including any that exist for special powers $p\neq0$. Third,
Noether's theorem is applied to obtain the conservation laws arising from the
Lie symmetries that are variational. Finally, explicit line soliton solutions
are derived for all powers $p>0$, and some of their properties are discussed.

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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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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: eess
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio