Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Waves over Curved Bottom: The Method of Composite Conformal Mapping   A compact and efficient numerical method is described for studying plane
flows of an ideal fluid with a smooth free boundary over a curved and
nonuniformly moving bottom. Exact equations of motion in terms of the so-called
conformal variables are used. In addition to the previously known applications
for shear flows with constant (including zero) vorticity, here a generalization
is made to the case of potential flows in uniformly rotating coordinate
systems, where centrifugal and Coriolis forces are added to the gravity force.
A brief review is given of previous results obtained by this method in a number
of physically interesting problems such as modeling of tsunami waves caused by
the movement of nonuniform bottom, the dynamics of Bragg (gap) solitons over a
spatially periodic bottom profile, the Fermi-Pasta-Ulam (FPU) recurrence
phenomenon for waves in a finite pool, the formation of anomalous waves in an
opposing nonuniform current, and the propagation of a solitary wave in a shear
current and its runup on a depth difference. In addition, a number of new
numerical results are presented concerning the nonlinear dynamics of a free
boundary in closed rotating containers partially filled with a fluid --
centrifuges of complex shape. In this case, the equations of motion differ in
some essential details from those of $x$-periodic systems.

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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin