Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On B\"{a}cklund transformations and boundary conditions associated with
  the quantum inverse problem for a discrete nonlinear integrable system and
  its connection to Baxter's Q-operator   A discrete nonlinear system is analysed in case of open chain boundary
conditions at the ends. It is shown that the integrability of the system
remains intact, by obtaining a modified set of Lax equations which
automatically take care of the boundary conditions. The same Lax pair also
conforms to the conditions stipulated by Sklyanin [5]. The quantum inverse
problem is set up and the diagonalisation is carried out by the method of
sparation of variables. B\"{a}cklund transformations are then derived under the
modified boundary conditions using the classical r-matrix . Finally by
quantising the B\"{a}cklund transformation it is possible to identify the
relation satisfied by the eigenvalue of Baxter's Q-operator even for the quasi
periodic situation.

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga