منابع مشابه
Supersymmetric Harry Dym Type Equations
A supersymmetric version is proposed for the well known Harry Dym system. A general class super Lax operator which leads to consistent equations is considered.
متن کاملAn extended Harry Dym hierarchy
Abstract An extended Harry Dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy associated with the pseudo-differential operator L = u∂ +u0 +u1∂−1 + · · ·. The corresponding Lax presentation possesses a self-consistent source involving squared eigenfunctions. The resulting extended Harry Dym hierarchy is reduced to t...
متن کامل2 On the Nonlocal Equations and Nonlocal Charges Associated with the Harry Dym Hierarchy
A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given.
متن کاملOn the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym equations
We show that the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym hierarchies can be obtained by applying a reduction process to a simple Poisson pair defined on the loop algebra of sl(2,R). The reduction process is a bi-Hamiltonian reduction, that can be canonically performed on every bi-Hamiltonian manifold.
متن کاملOn the Bi-hamiltonian Theory for the Harry Dym Equation
We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg-de Vries equation and other soliton equations. This is achieved by means of a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev-Petviashivili hierarchy whose reduction leads to the Harry Dym hierarchy. We call such system the HD-KP hi...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1995
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/28/8/004