Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic
  Travelling Waves   The paper deals with a problem of interaction between hydrodynamics and
mechanics of nonlinear elastic bodies. The existence question for
two-dimensional symmetric steady waves travelling on the surface of a deep
ocean beneath a heavy elastic membrane is analyzed as a problem in bifurcation
theory. The behaviour of the two-dimensional cross-section of the membrane is
modelled as a thin (unshearable), heavy, hyperelastic Cosserat rod, following
Antman's elasticity theory, and the fluid beneath is supposed to be in steady
2D irrotational motion under gravity. Assuming that gravity and the density of
the undeformed membrane are prescribed, the free parameters of the problem are
the speed of the wave and drift velocity of the membrane.
  The analysis relies upon a conformal formulation of the hydro-elastic problem
developed in previous papers; the basic tool for the study of the bifurcation
picture is the implicit function theorem, under some non-resonance assumptions.
  The most interesting part of the final result is the existence of a
symmetry-breaking 'third sheet' of solutions, which bifurcates from primary
sheets, and is a hydro-elastic analogue of the phenomenon known as 'Wilton
ripples' in the surface tension case.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs