Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dissipative periodic waves, solitons and breathers of the nonlinear
  Schrodinger equation with complex potentials   Exact solutions for the generalized nonlinear Schr\"odinger (NLS) equation
with inhomogeneous complex linear and nonlinear potentials are found. We have
found localized and periodic solutions for a wide class of localized and
periodic modulations in the space of complex potentials and nonlinearity
coefficients. Examples of stable and unstable solutions are given. We also
demonstrated numerically the existence of stable dissipative breathers in the
presence of an additional parabolic trap.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th