Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modulations of viscous fluid conduit periodic waves   In this work, modulation of periodic interfacial waves on a conduit of
viscous liquid is explored utilizing Whitham theory and Nonlinear Schr\"odinger
(NLS) theory. Large amplitude periodic wave modulation theory does not require
integrability of the underlying model equation, yet in practice, either
integrable equations are studied or the full extent of Whitham (wave-averaging)
theory is not developed. The governing conduit equation is nonlocal with
nonlinear dispersion and is not integrable. Via a scaling symmetry, periodic
waves can be characterized by their wavenumber and amplitude. In the weakly
nonlinear regime, both the defocusing and focusing variants of the NLS equation
are derived, depending on the wavenumber. Dark and bright envelope solitons are
found to persist in the conduit equation. Due to non-convex dispersion,
modulational instability for periodic waves above a critical wavenumber is
predicted. In the large amplitude regime, structural properties of the Whitham
modulation equations are computed, including strict hyperbolicity, genuine
nonlinearity, and linear degeneracy. Bifurcating from the NLS critical
wavenumber at zero amplitude is an amplitude-dependent elliptic region for the
Whitham equations within which a maximally unstable periodic wave is
identified. These results have implications for dispersive shock waves,
recently observed experimentally.

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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph