Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation

Details Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation

2010-08-12

arxiv.org/abs/1008.2128v3

Physics

Mathematical Physics

41 pages, minor corrections, Section 5 revised

Scientific paper

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.

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