Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degenerate weakly nonlinear elastic plane waves   Weakly nonlinear plane waves are considered in hyperelastic crystals.
Evolution equations are derived at a quadratically nonlinear level for the
amplitudes of quasi-longitudinal and quasi-transverse waves propagating in
arbitrary anisotropic media. The form of the equations obtained depends upon
the direction of propagation relative to the crystal axes. A single equation is
found for all propagation directions for quasi-longitudinal waves, but a pair
of coupled equations occurs for quasi-transverse waves propagating along
directions of degeneracy, or acoustic axes. The coupled equations involve four
material parameters but they simplify if the wave propagates along an axis of
material symmetry. Thus, only two parameters arise for propagation along an
axis of two-fold symmetry, and one for a three-fold axis. The transverse wave
equations decouple if the axis is four-fold or higher. In the absence of a
symmetry axis it is possible that the evolution equations of the
quasi-transverse waves decouple if the third order elastic moduli satisfy a
certain identity. The theoretical results are illustrated with explicit
examples.

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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs