Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-dimensional position-dependent mass Lagrangians; Superintegrability
  and exact solvability   The two-dimensional extension of the one-dimensional PDM-Lagrangians and
their nonlocal point transformation mappings into constant unit-mass exactly
solvable Lagrangians is introduced. The conditions on the related
two-dimensional Euler-Lagrange equations' invariance are reported. The mappings
from superintegrable linear oscillators into sub-superintegrable nonlinear
PDM-oscillators are exemplified by, (i) a sub-superintegrable
Mathews-Lakshmanan type-I PDM-oscillator, for a PDM-particle moving in a
harmonic oscillator potential, (ii) a sub-superintegrable Mathews-Lakshmanan
type-II PDM-oscillator, for a PDM-particle moving in a constant potential, and
(iii) a sub-superintegrable shifted Mathews-Lakshmanan type-III PDM-oscillator,
for a PDM-particle moving in a shifted harmonic oscillator potential. Moreover,
the superintegrable shifted linear oscillators and the isotonic oscillators are
mapped into a sub-superintegrable PDM-nonlinear and a sub-superintegrable
PDM-isotonic oscillators, respectively.

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The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg