Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Traveling waves for a quasilinear wave equation   We consider a 2+1 dimensional wave equation appearing in the context of
polarized waves for the nonlinear Maxwell equations. The equation is
quasilinear in the time derivatives and involves two material functions $V$ and
$\Gamma$. We prove the existence of traveling waves which are periodic in the
direction of propagation and localized in the direction orthogonal to the
propagation direction. Depending on the nature of the nonlinearity coeffcient
$\Gamma$ we distinguish between two cases: (a) $\Gamma\in L^\infty$ being
regular and (b) $\Gamma=\gamma\delta_0$ being a multiple of the delta potential
at zero. For both cases we use bifuraction theory to prove the existence of
nontrivial small-amplitude solutions. One can regard our results as a
persistence result which shows that guided modes known for linear wave-guide
geometries survive in the presence of a nonlinear constitutive law. Our main
theorems are derived under a set of conditions on the linear wave operator.
They are subsidised by explicit examples for the coefficients $V$ in front of
the (linear) second time derivative for which our results hold.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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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: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: physics