Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation
Mathematical Physics
2010-09-17 v3 math.MP
Exactly Solvable and Integrable Systems
Abstract
We consider a Frobenius structure associated with the dispersionless Kadomtsev-Petviashvili equation. This is done, essentially, by applying a continuous analogue of the finite dimensional theory in the space of Schwartz functions on the line. The potential of the Frobenius manifold is found to be a logarithmic potential with quadratic external field. Following the construction of the principal hierarchy, we construct a set of infinitely many commuting flows, which extends the classical dKP hierarchy.
Keywords
Cite
@article{arxiv.1008.2128,
title = {Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation},
author = {Andrea Raimondo},
journal= {arXiv preprint arXiv:1008.2128},
year = {2010}
}
Comments
41 pages, minor corrections, Section 5 revised