Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay in the one dimensional generalized Improved Boussinesq equation   We consider the decay problem for the generalized improved (or regularized)
Boussinesq model with power type nonlinearity, a modification of the originally
ill-posed shallow water waves model derived by Boussinesq. This equation has
been extensively studied in the literature, describing plenty of interesting
behavior, such as global existence in the space $H^1\times H^2$, existence of
super luminal solitons, and lack of a standard stability method to describe
perturbations of solitons. The associated decay problem has been studied by
Liu, and more recently by Cho-Ozawa, showing scattering in weighted spaces
provided the power of the nonlinearity $p$ is sufficiently large. In this paper
we remove that condition on the power $p$ and prove decay to zero in terms of
the energy space norm $L^2\times H^1$, for any $p>1$, in two almost
complementary regimes: (i) outside the light cone for all small, bounded in
time $H^1\times H^2$ solutions, and (ii) decay on compact sets of arbitrarily
large bounded in time $H^1\times H^2$ solutions. The proof consists in finding
two new virial type estimates, one for the exterior cone problem based in the
energy of the solution, and a more subtle virial identity for the interior cone
problem, based in a modification of the momentum.

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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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: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph