2006/04/30 by Guido Carlet · 2 citations
Physics and Astronomy · Mathematics · #math-ph #math.DG #math.MP #msc:37K10 #msc:53D45
paper · pdf · doi:10.1088/0305-4470/39/30/003
published as J. Phys. A: Math. Gen. 39 (2006) 9411-9435 · 32 pages, corrected typos
arxiv created 2008/11/04 · arxiv updated 2009/12/01
We generalize the Toda lattice hierarchy by considering N+M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that are ε-series of differential polynomials in the dependent variables, and we use them to provide a Lax pair definition of the extended bigraded Toda hierarchy. Using R-matrix theory we give the bihamiltonian formulation of this hierarchy and we prove the existence of a tau function for its solutions. Finally we study the dispersionless limit and its connection with a class of Frobenius manifolds on the orbit space of the extended affine Weyl groups of the A series.