%0 Journal Article %J Communications in Mathematical Physics 311 (2012) 557-594 %D 2012 %T Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation %A Andrea Raimondo %X 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. %B Communications in Mathematical Physics 311 (2012) 557-594 %I Springer %G en %U http://hdl.handle.net/1963/6040 %1 5931 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-07-31T12:51:57Z\\nNo. of bitstreams: 1\\n1008.2128v3.pdf: 349185 bytes, checksum: a5a3fa842d50f3d9450813e55218f093 (MD5) %R 10.1007/s00220-012-1470-7 %0 Journal Article %J J. Phys. A 43 (2010) 045201 %D 2010 %T The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures %A Guido Carlet %A Paolo Lorenzoni %A Andrea Raimondo %X 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. %B J. Phys. A 43 (2010) 045201 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/3846 %1 863 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-17T09:13:18Z\\nNo. of bitstreams: 1\\n0910.1210v1.pdf: 183431 bytes, checksum: 90f5253ca8e81822f6ffb26ece621075 (MD5) %R 10.1088/1751-8113/43/4/045201