TY - RPRT
T1 - Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
Y1 - 2015
A1 - Guido Carlet
A1 - Matteo Casati
A1 - Sergey Shadrin
AB - We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D>1. Hence, in contrast with the D=1 case, the deformation theory in the multivariable case is non-trivial.
U1 - 35389
U2 - Mathematics
U4 - 1
U5 - MAT/03
ER -
TY - JOUR
T1 - Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems
JF - Matematische Annalen 349 (2011) 75-115
Y1 - 2011
A1 - Guido Carlet
A1 - Boris Dubrovin
A1 - Luca Philippe Mertens
AB - We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.
PB - Springer
UR - http://hdl.handle.net/1963/3584
U1 - 716
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures
JF - J. Phys. A 43 (2010) 045201
Y1 - 2010
A1 - Guido Carlet
A1 - Paolo Lorenzoni
A1 - Andrea Raimondo
AB - We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.
PB - IOP Publishing
UR - http://hdl.handle.net/1963/3846
U1 - 863
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The Extended Toda Hierarchy
JF - Moscow Math. J. 4 (2004)\\n313-332.
Y1 - 2004
A1 - Guido Carlet
A1 - Boris Dubrovin
A1 - Zhang Youjin
UR - http://hdl.handle.net/1963/2542
U1 - 1577
U2 - Mathematics
U3 - Mathematical Physics
ER -