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

@article{Ma1998ACO, title={A CLASS OF COUPLED KDV SYSTEMS AND THEIR BI-HAMILTONIAN FORMULATION}, author={Wenxiu Ma}, journal={Journal of Physics A}, year={1998}, volume={31}, pages={7585-7591} }

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 the systems leads to the KdV hierarchy. Illustrative examples are given.

## 29 Citations

Hamiltonian structure of multi component integrable systems

- Physics
- 2001

In this work we have generalized the super KdV equation into a multicomponent super KdV equation. It is shown that the system is bi-super Hamiltonian. The third super Hamiltonian in the…

On the Bi-Hamiltonian Structure of the KdV Hierarchy

- Physics
- 2003

A construction procedure is derived to obtain expressions for Hamiltonian densities which characterize the bi-Hamiltonian structure of the equations in the KdV hierarchy. All results are obtained by…

Extending Hamiltonian operators to get bi-Hamiltonian coupled KdV systems

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- 1998

Multi-component bi-super Hamiltonian KdV systems

- Physics
- 2001

It is shown that a new class of classical multi-component super KdV equations is bi-super Hamiltonian by extending the method for the verification of graded Jacobi identity. The multi-component…

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

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- 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…

TWO FAMILIES GENERALIZATION OF AKNS HIERARCHIES AND THEIR HAMILTONIAN STRUCTURES

- Mathematics
- 2010

By means of the Lie algebra G1, we construct an extended Lie algebra G2. Two different isospectral problems are designed by the two different Lie algebra G1 and G2. With the help of the variational…

The Integrability of New Two-Component KdV Equation ?

- Physics
- 2010

We consider the bi-Hamiltonian representation of the two-component coup- led KdV equations discovered by Drinfel'd and Sokolov and rediscovered by Sakovich and Foursov. Connection of this equation…

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…

Integrable Couplings of the Generalized AKNS Hierarchy with an Arbitrary Function and Its Bi-Hamiltonian Structure

- Mathematics, Physics
- 2007

Abstract
We construct a new loop algebra
$\widetilde{A_{3}}$
, which is used to set up an isospectral problem. Then a new integrable couplings of the generalized AKNS hierarchy is derived, which…

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