Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solutions of multicomponent nonlinear Schr\"odinger equations
  under general plane-wave boundary conditions   We construct exact soliton solutions of integrable multicomponent nonlinear
Schr\"odinger (NLS) equations under general nonvanishing boundary conditions.
Different components of the vector (or matrix) dependent variable can approach
plane waves with different wavenumbers and frequencies at spatial infinity. We
apply B\"acklund-Darboux transformations to the cubic NLS equations with a
self-focusing nonlinearity, a self-defocusing nonlinearity or a mixed
focusing-defocusing nonlinearity. Both bright-soliton solutions and
dark-soliton solutions are obtained, depending on the signs of the nonlinear
terms and the type of B\"acklund-Darboux transformation. The multicomponent
solitons generally possess internal degrees of freedom and provide highly
nontrivial generalizations of the scalar NLS solitons. The main step in the
construction of the multicomponent solitons is to compute the matrix
exponential of a constant non-diagonal matrix arising from the Lax pair. With a
suitable re-parametrization of the non-diagonal matrix, the matrix exponential
can be computed explicitly in closed form for the most interesting cases such
as the two-component vector NLS equation. In particular, we do not resort to
Cardano's formula in diagonalizing a $3 \times 3$ matrix, so our expressions
for the multicomponent solitons are in some sense more explicit and useful than
those obtained in [Q-H. Park and H. J. Shin, Phys. Rev. E 61 (2000) 3093].

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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph