Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Oscillatory solitons of U(1)-invariant mKdV equations II: Asymptotic
  behavior and constants of motion   The Hirota equation and the Sasa-Satsuma equation are U(1)-invariant
integrable generalizations of the modified Korteweg-de Vries equation. These
two generalizations admit oscillatory solitons, which describe harmonically
modulated complex solitary waves parameterized by their speed, modulation
frequency, and phase. Depending on the modulation frequency, the speeds of
oscillatory waves (1-solitons) can be positive, negative, or zero, in contrast
to the strictly positive speed of ordinary solitons. When the speed is zero, an
oscillatory wave is a time-periodic standing wave. Oscillatory 2-solitons with
non-zero wave speeds are shown to describe overtake collisions of a fast wave
and a slow wave moving in the same direction, or head-on collisions of two
waves moving in opposite directions. When one wave speed is zero, oscillatory
2-solitons are shown to describe collisions in which a moving wave overtakes a
standing wave. An asymptotic analysis using moving coordinates is carried out
to show that, in all collisions, the speeds and modulation frequencies of the
individual waves are preserved, while the phases and positions undergo a shift
such that the center of momentum of the two waves moves at a constant speed.
The primary constants of motion as well as some other features of the nonlinear
interaction of the colliding waves are discussed.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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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: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ