Bi-Hamiltonian aspects of a matrix Harry Dym hierarchy
نویسندگان
چکیده
منابع مشابه
Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy
We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy, which permits us to define a matrix Harry Dym hierarchy. We conclude by showing that the conserved densities of the matrix Harry Dym equation can be found by means of a Riccati-type equation.
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...
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 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 کاملThe debar-approach to the Dispersionless Harry-Dym Hierarchy
A debarapproach is adopted to study the dispersionless Harry-Dym (dHD) hierarchy. Moreover, this formulism is applied to construct some explicit solutions of the dHD hierarchy.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2008
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2982232