Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis and comparative study of non-holonomic and quasi-integrable
  deformations of the Nonlinear Schr\"odinger Equation   The non-holonomic deformation of the nonlinear Schr\"odinger equation,
uniquely obtained from both the Lax pair and Kupershmidt's bi-Hamiltonian
[Phys. Lett. A 372, 2634 (2008)] approaches, is compared with the
quasi-integrable deformation of the same system [Ferreira et. al. JHEP 2012,
103 (2012)]. It is found that these two deformations can locally coincide only
when the phase of the corresponding solution is discontinuous in space,
following a definite phase-modulus coupling of the non-holonomic inhomogeneity
function. These two deformations are further found to be not gauge-equivalent
in general, following the Lax formalism of the nonlinear Schr\"odinger
equation. However, asymptotically they converge for localized solutions as
expected. Similar conditional correspondence of nonholonomic deformation with a
non-integrable deformation, namely, due to local scaling of the amplitude of
the nonlinear Schr\"odinger equation is further obtained.

22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph