Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers
  Equation with Movement Direction as a Variable   We study self-propelled particles by direct numerical simulation of the
nonlinear Kramers equation for self-propelled particles. In our previous paper,
we studied self-propelled particles with velocity variables in one dimension.
In this paper, we consider another model in which each particle exhibits
directional motion. The movement direction is expressed with a variable $\phi$.
We show that one-dimensional solitary wave states appear in direct numerical
simulations of the nonlinear Kramers equation in one- and two-dimensional
systems, which is a generalization of our previous result. Furthermore, we find
two-dimensionally localized states in the case that each self-propelled
particle exhibits rotational motion. The center of mass of the
two-dimensionally localized state exhibits circular motion, which implies
collective rotating motion. Finally, we consider a simple one-dimensional model
equation to qualitatively understand the formation of the solitary wave state.

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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga