TY - JOUR
T1 - Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation
JF - Communications in Mathematical Physics 311 (2012) 557-594
Y1 - 2012
A1 - Andrea Raimondo
AB - We consider a Frobenius structure associated with the dispersionless\\r\\nKadomtsev-Petviashvili equation. This is done, essentially, by applying a\\r\\ncontinuous analogue of the finite dimensional theory in the space of Schwartz\\r\\nfunctions on the line. The potential of the Frobenius manifold is found to be a\\r\\nlogarithmic potential with quadratic external field. Following the construction\\r\\nof the principal hierarchy, we construct a set of infinitely many commuting\\r\\nflows, which extends the classical dKP hierarchy.
PB - Springer
UR - http://hdl.handle.net/1963/6040
U1 - 5931
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
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 -