Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations
2007 ◽
Vol 365
(1858)
◽
pp. 2333-2357
◽
Keyword(s):
This paper is a survey article on bi-Hamiltonian systems on the dual of the Lie algebra of vector fields on the circle. Here, we investigate the special case where one of the structures is the canonical Lie–Poisson structure and the second one is constant. These structures, called affine or modified Lie–Poisson structures, are involved in the integrability of certain Euler equations that arise as models for shallow water waves.
1987 ◽
Vol 10
(3)
◽
pp. 557-562
◽
2020 ◽
Vol 76
(2)
◽
pp. I_565-I_570
Keyword(s):
Keyword(s):
Keyword(s):
2000 ◽
Vol 24
(10)
◽
pp. 649-661
◽
2015 ◽
Vol 258
(12)
◽
pp. 4103-4126
◽
Keyword(s):