Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solitons Riding on Solitons: Hypersolitons and the Quantum Newton's
  Cradle   The reduced dynamics for dark and bright soliton chains in the
one-dimensional nonlinear Schr\"odinger equation is used to study the behavior
of collective compression waves. For appropriate conditions, the reduced
dynamics derived from perturbation and variational techniques allows to
describe a chain of dark or bright solitons as a chain of effective masses
connected by nonlinear springs taking the form of a Toda lattice model on the
soliton's positions. In turn, the Toda lattice possesses exact solitary
travelling compression wave solutions corresponding to travelling compression
waves in the original soliton chain. We coin the term hypersoliton to describe
such solitary waves riding on a chain of solitons. We corroborate our
analytical results with direct numerical simulations of the nonlinear
Schr\"odinger equation. It is observed that in the case of dark soliton chains,
the formulated reduction dynamics provides an accurate description for the
robust evolution of travelling compression waves. In contrast, bright soliton
chains do not have such stable propagating solutions due to the
desynchronization of the mutual phases between consecutive solitons during
evolution. Finally, as an application to Bose-Einstein condensates trapped in a
standard external harmonic trapping potential, we study the case of finite dark
soliton chain confined at the center of the trap. We find that when the central
chain is hit by a dark soliton initiated at the edge of the external trap, the
energy is transferred through the chain as a hypersoliton. When the
hypersoliton reaches the end of the central chain, a dark soliton is ejected
away from the center of the trap and, as it returns from its excursion up the
trap, hits the central chain producing again a hypersoliton. This periodic
evolution is the equivalent of the classical Newton's cradle.

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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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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: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph