Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some new integrable systems constructed from the bi-Hamiltonian systems
  with pure differential Hamiltonian operators   When both Hamiltonian operators of a bi-Hamiltonian system are pure
differential operators, we show that the generalized Kupershmidt deformation
(GKD) developed from the Kupershmidt deformation in \cite{kd} offers an useful
way to construct new integrable system starting from the bi-Hamiltonian system.
We construct some new integrable systems by means of the generalized
Kupershmidt deformation in the cases of Harry Dym hierarchy, classical
Boussinesq hierarchy and coupled KdV hierarchy. We show that the GKD of Harry
Dym equation, GKD of classical Boussinesq equation and GKD of coupled KdV
equation are equivalent to the new integrable Rosochatius deformations of these
soliton equations with self-consistent sources. We present the Lax Pair for
these new systems. Therefore the generalized Kupershmidt deformation provides a
new way to construct new integrable systems from bi-Hamiltonian systems and
also offers a new approach to obtain the Rosochatius deformation of soliton
equation with self-consistent sources.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an