91 20 16 v 1 2 9 D ec 1 99 9 On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies
نویسنده
چکیده
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.
منابع مشابه
A pr 2 00 4 On the r - th dispersionless Toda hierarchy I : Factorization problem , symmetries and some solutions
For a family of Poisson algebras, parametrized by r ∈ Z, and an associated Lie algebraic splitting, we consider the factorization of given canonical transformations. In this context we rederive the recently found r-th dispersionless modified KP hierachies and r-th dispersionless Dym hierarchies, giving a new Miura map among them. We also found a new integrable hierarchy which we call the r-th d...
متن کامل0 M ay 2 00 4 On the r - th dispersionless Toda hierarchy I : Factorization problem , symmetries and some solutions Manuel
For a family of Poisson algebras, parametrized by r ∈ Z, and an associated Lie algebraic splitting, we consider the factorization of given canonical transformations. In this context we rederive the recently found r-th dispersionless modified KP hierachies and r-th dispersionless Dym hierarchies, giving a new Miura map among them. We also found a new integrable hierarchy which we call the r-th d...
متن کامل0 M ay 2 00 4 On the r - th dispersionless Toda hierarchy I : Factorization problem , symmetries and some solutions
For a family of Poisson algebras, parametrized by r ∈ Z, and an associated Lie algebraic splitting, we consider the factorization of given canonical transformations. In this context we rederive the recently found r-th dispersionless modified KP hierachies and r-th dispersionless Dym hierarchies, giving a new Miura map among them. We also found a new integrable hierarchy which we call the r-th d...
متن کامل2 M ay 2 00 4 S - functions , reductions and hodograph solutions of the r - th dispersionless modified KP and Dym hierarchies
We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these S-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the S-function formulation leads to hodograph systems for the associated solutions. We consider ...
متن کاملv - in t / 9 90 70 19 v 1 2 2 Ju l 1 99 9 Miura Map between Lattice KP and its Modification is Canonical
We consider the Miura map between the lattice KP hierarchy and the lattice modified KP hierarchy and prove that the map is canonical not only between the first Hamiltonian structures, but also between the second Hamiltonian structures.
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