Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A PT-symmetric dual-core system with the sine-Gordon nonlinearity and
  derivative coupling   We propose a system of sine-Gordon equations, with the $\mathcal{PT}$
symmetry represented by balanced gain and loss in them. The equations are
coupled by sine-field terms and first-order derivatives. The sinusoidal
coupling stems from local interaction between adjacent particles in the coupled
Frenkel-Kontorova (FK) chains and related sine-lattices, while the
cross-derivative coupling, which was not considered before, is induced by
\emph{three-particle} interactions, provided that the particles in the parallel
FK\ chains move in different directions. Nonlinear wave structures are then
studied in this model. In particular, kink-kink (KK) and kink-antikink (KA)
complexes are explored by means of analytical and numerical methods. It is
predicted analytically and confirmed numerically that the complexes are
unstable for one sign of the sinusoidal coupling, and stable for another.
Stability regions are delineated in the underlying parameter space. Unstable
complexes split into free kinks/antikinks that may propagate or become
stationary, depending on whether they are subject to gain or loss,
respectively.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg