In this paper we construct a class of integrable Hamiltonian nonlinear evolution equations generated by a purely differential recursion operator. It turns out that this hierarchy is a complex version of the Burgers hierarchy and can be linearized through a generalization of the Cole–Hopf transformation.
Topics
Hamiltonian mechanics
REFERENCES
1.
See, for instance, the basic works of
V. E.
Zakharov
and L. D.
Faddeev
, Funct. Anal. Appl.
5
, 280
(1971
);2.
3.
A table of the recursion operators for the more relevant integrable NEE’s can be found in
F.
Magri
, Lect. Notes Phys.
120
, 233
(1980
).4.
D. V.
Choodnovsky
and G. V.
Choodnovsky
, Nuovo Cimento B
40
, 339
(1977
).5.
D.
Levi
, O.
Ragnisco
, and M.
Bruschi
, Nuovo Cimento B
74
, 33
(1983
).6.
D. R. Lebedev and Yu. A. Manin, “Gel’Fand‐Dikii Hamiltonian operator and coadjoint representation of Volterra group” (to appear);
7.
F. Magri and C. Morosi, “A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson‐Nijenhuis manifolds,” Preprint Universită di Milano (to appear).
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© 1985 American Institute of Physics.
1985
American Institute of Physics
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