An r‐matrix formalism is applied to the construction of the integrable lattice systems and their bi‐Hamiltonian structure. Miura‐like gauge transformations between the hierarchies are also investigated. In the end the ladder of linear maps between generated hierarchies is established and described.  

1.
B. A. Kupershmidt, Asterisque 123 (1985).
2.
. Ragnisco and P. M. Santini, A unified algebraic approach to the integrable and discrete evolution equations, Preprint No. 668, Department of Physics, Rome University, 1989.
3.
T.
Gui-Zhang
,
J. Phys. A
23
,
3903
(
1990
).
4.
W.
Oevel
,
G.
Zhang
, and
B.
Fuchssteiner
,
Prog. Theor. Phys.
81
,
294
(
1989
).
5.
E. K. Sklyanin, Preprint LOMI, E-3-79, Leningrad, 1980.
6.
M. A.
Semenov-Tian-Shansky
,
Func. Anal. Appl.
17
,
17
(
1983
).
7.
M.
Adler
,
Invent. Math.
50
,
219
(
1979
).
8.
B.
Kostant
,
Adv. Math.
34
,
195
(
1979
).
9.
B. A.
Kupershmidt
,
Commun. Math. Phys.
99
,
51
(
1985
).
10.
W.
Oevel
,
J. Math. Phys.
30
,
1140
(
1989
).
11.
W.
Oevel
and
O.
Ragnisco
,
Physica A
161
,
181
(
1989
).
12.
B. G.
Konopelchenko
and
W.
Oevel
,
Publ. RIMS, Kyoto Univ.
29
,
581
(
1993
).
13.
J. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, New York, 1986).
14.
A.
Weinstein
,
J. Diff. Geom.
18
,
523
(
1983
).
15.
M. Toda, Theory of Nonlinear Lattice (Springer-Verlag, New York, 1981).
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