Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collision of $\phi^4$ kinks free of the Peierls-Nabarro barrier in the
  regime of strong discreteness   The two major effects observed in collisions of the continuum $\phi^4$ kinks
are (i) the existence of critical collision velocity above which the kinks
always emerge from the collision and (ii) the existence of the escape windows
for multi-bounce collisions with the velocity below the critical one,
associated with the energy exchange between the kink's internal and
translational modes. The potential merger (for sufficiently low collision
speeds) of the kink and antikink produces a bion with oscillation frequency
$\omega_B$, which constantly radiates energy, since its higher harmonics are
always within the phonon spectrum. Similar effects have been observed in the
discrete $\phi^4$ kink-antikink collisions for relatively weak discreteness.
Here we analyze kinks colliding with their mirror image antikinks in the regime
of strong discreteness considering an exceptional discretization of the
$\phi^4$ field equation where the static Peierls-Nabarro potential is precisely
zero and the not-too-fast kinks can propagate practically radiating no energy.
Several new effects are observed in this case, originating from the fact that
the phonon band width is small for strongly discrete lattices and for even
higher discreteness an inversion of the phonon spectrum takes place with the
short waves becoming low-frequency waves. When the phonon band is narrow, not a
bion but a discrete breather with frequency $\omega_{DB}$ and all higher
harmonics outside the phonon band is formed. When the phonon spectrum is
inverted, the kink and antikink become mutually repulsive solitary waves with
oscillatory tails, and their collision is possible only for velocities above a
threshold value sufficient to overcome their repulsion.

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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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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: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci