## 30 Citations

A Difference Hamiltonian Operator and a Hierarchy of Generalized Toda Lattice Equations

- Physics, Mathematics
- 2005

A difference Hamiltonian operator with three arbitrary constants is presented. When the arbitrary constants in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given.…

A three-parameter difference Hamiltonian operator, corresponding pair of Hamiltonian operators and a family of Liouville integrable lattice equations

- Mathematics, Physics
- 2010

On a class of coupled Hamiltonian operators and their integrable hierarchies with two potentials

- Mathematics
- 2018

We discuss at first in this paper the Gauge equivalence among several u‐linear Hamiltonian operators and present explicitly the associated Gauge transformation of Bäcklund type among them. We then…

A bi-Hamiltonian formulation for triangular systems by perturbations

- Mathematics, Physics
- 2002

A bi-Hamiltonian formulation is proposed for triangular systems resulting from perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems…

TWO SUPER-INTEGRABLE SYSTEMS AND ASSOCIATED SUPER-HAMILTONIAN STRUCTURES

- Mathematics, Physics
- 2009

The super extensions of g-cKdV and mKdV integrable systems are proposed. Two hierarchies of super-integrable nonlinear evolution equations are found. In addition, making use of the super-trace…

Component-trace identities for Hamiltonian structures

- Mathematics
- 2010

We show that on a particular class of semi-direct sums of matrix Lie algebras, component traces of the matrix product can produce bilinear forms which are non-degenerate, symmetric and invariant…

New Soliton Hierarchies Associated with the Lie Algebra so(3,ℝ) and their BI-Hamiltonian Structures

- Mathematics
- 2015

A HIERARCHY OF SOLITON EQUATIONS ASSOCIATED WITH A HIGHER-DIMENSIONAL LOOP ALGEBRA AND ITS TRI-HAMILTONIAN STRUCTURE

- Mathematics
- 2008

A new higher-dimensional loop algebra is given for which a Lax isospectral problem is set up whose compatibility condition gives rise to a Liouville integrable soliton hierarchy along with…

New non-isospectral integrable couplings of the AKNS system

- Mathematics, PhysicsAppl. Math. Comput.
- 2008

## References

SHOWING 1-10 OF 40 REFERENCES

THE BI-HAMILTONIAN STRUCTURE OF THE PERTURBATION EQUATIONS OF THE KDV HIERARCHY

- Physics, Mathematics
- 1996

A CLASS OF COUPLED KDV SYSTEMS AND THEIR BI-HAMILTONIAN FORMULATION

- Physics
- 1998

A Hamiltonian pair is proposed and thus a type of hereditary operators results. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of…

Extending the Hamiltonian structures and new integrable systems

- Physics, Mathematics
- 1994

By starting with the known Hamiltonian structure of integrable systems, it is shown how extended Hamiltonian operators can be constructed using the conditions deduced by Dorfman for an operator to be…

Quasiclassical limit of coupled KdV equations: Riemann invariants and multi-Hamiltonian structure

- Mathematics, Physics
- 1991

Extension of hereditary symmetry operators

- Mathematics
- 1998

Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commuting symmetries may be generated. Some…

Integrable coupled KdV systems

- Mathematics, Physics
- 1998

We give the conditions for a system of N-coupled Korteweg de Vries (KdV) type of equations to be integrable. We find the recursion operators of each subclass and give all examples for N=2.

On the structure of symplectic operators and hereditary symmetries

- Mathematics
- 1980

In the last fifteen years, there has been a remarlmble development in the exact analysis of certain nonlinear evolution equations, like tbe Korteweg-de Vries equation. I t is weH known that among the…