Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transition fronts and their universality classes   Steadily moving transition (switching) fronts, bringing local transformation,
symmetry breaking or collapse, are among the most important dynamic coherent
structures. The nonlinear mechanical waves of this type play a major role in
many modern applications involving the transmission of mechanical information
in systems ranging from crystal lattices and metamaterials to macroscopic civil
engineering structures. While many different classes of such dynamic fronts are
known, the interrelation between them remains obscure. Here we consider a
minimal prototypical mechanical system, the Fermi-Pasta-Ulam (FPU) chain with
piecewise linear nonlinearity, and show that there are exactly three distinct
classes of switching fronts, which differ fundamentally in how (and whether)
they produce and transport oscillations. The fact that all three types of
fronts could be obtained as explicit Wiener-Hopf solutions of the same discrete
FPU problem, allows one to identify the exact mathematical origin of the
particular features of each class. To make the underlying Hamiltonian dynamics
analytically transparent, we construct a minimal quasicontinuum approximation
of the FPU model that captures all three classes of the fronts and
interrelation between them. This approximation is of higher order than
conventional ones (KdV, Boussinesq) and involves mixed space-time derivatives.
The proposed framework unifies previous attempts to classify the mechanical
transition fronts as radiative, dispersive, topological or compressive and
categorizes them instead as different types of dynamic lattice defects.

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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: econ