On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies

Abstract

We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and Takebe, the twistor construction of solution structure for the dispersionless modified KP hierarchy is given.

19 pages, Latex, no figures

References in corpus (1)

• Classical $\mathbf{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras

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