Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing Traveling Wave Collisions in Granular Chains Starting
  from Integrable Limits: the case of the KdV and the Toda Lattice   Our aim in the present work is to develop approximations for the collisional
dynamics of traveling waves in the context of granular chains in the presence
of precompression. To that effect, we aim to quantify approximations of the
relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV)
equation and the Toda lattice. Using the availability in such settings of both
1-soliton and 2-soliton solutions in explicit analytical form, we initialize
such coherent structures in the granular chain and observe the proximity of the
resulting evolution to the underlying integrable (KdV or Toda) model. While the
KdV offers the possibility to accurately capture collisions of solitary waves
propagating in the same direction, the Toda lattice enables capturing both
co-propagating and counter-propagating soliton collisions. The error in the
approximation is quantified numerically and connections to bounds established
in the mathematical literature are also given.

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The categories of this paper are: funct-an
18
The categories of this paper are: econ
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn