Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New integrable boundary conditions for the Ablowitz-Ladik model: from
  Hamiltonian formalism to nonlinear mirror image method   Using Sklyanin's classical theory of integrable boundary conditions, we use
the Hamiltonian approach to derive new integrable boundary conditions for the
Ablowitz-Ladik model on the finite and half infinite lattice. In the case of
half infinite lattice, the special and new emphasis of this paper is to connect
directly the Hamiltonian approach, based on the classical $r$-matrix, with the
zero curvature representation and B\"acklund transformation approach that
allows one to implement a nonlinear mirror image method and construct explicit
solutions. It is shown that for our boundary conditions, which generalise
(discrete) Robin boundary conditions, a nontrivial extension of the known
mirror image method to what we call {\it time-dependent boundary conditions} is
needed. A careful discussion of this extension is given and is facilitated by
introducing the notion of intrinsic and extrinsic picture for describing
boundary conditions. This gives the specific link between Sklyanin's reflection
matrices and B\"acklund transformations combined with folding, {\it in the case
of non-diagonal reflection matrices}. All our results reproduce the known Robin
boundary conditions setup as a special case: the diagonal case. Explicit
formulas for constructing multisoliton solutions on the half-lattice with our
time-dependent boundary conditions are given and some examples are plotted.

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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cs