# The multi-component nonisospectral KdV hierarchies associated with a novel kind of N-dimensional Lie algebra

@inproceedings{Wang2022TheMN, title={The multi-component nonisospectral KdV hierarchies associated with a novel kind of N-dimensional Lie algebra}, author={Haifeng Wang}, year={2022} }

: A new class of N -dimensional Lie algebra is constructed to generate multi-component hierarchy of soliton equations. In this paper, we consider a nonisospectral problem, from which we obtain a nonisospectral KdV integrable hierarchy. Then, we deduce a coupled nonisospectral KdV hierarchy by means of the corresponding higher-dimensional loop algebra. It follows that the K symmetries, τ symmetries and their Lie algebra of the coupled nonisospectral KdV hierarchy are investigated. The bi…

## References

SHOWING 1-10 OF 50 REFERENCES

### A new multi-component integrable coupling and its application to isospectral and nonisospectral problems

- MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2022

### A kind of nonisospectral and isospectral integrable couplings and their Hamiltonian systems

- Mathematics, PhysicsCommun. Nonlinear Sci. Numer. Simul.
- 2021

### An approach for constructing nonisospectral hierarchies of evolution equations

- Mathematics
- 1992

For a given isospectral ( lambda t=0) hierarchy of evolution equations, the author proposes a simple method of constructing its corresponding nonisospectral ( lambda t= lambda n,n>or=0) hierarchy of…

### An integrable coupling hierarchy of the Mkdv_integrable systems, its Hamiltonian structure and corresponding nonisospectral integrable hierarchy

- Mathematics, PhysicsAppl. Math. Comput.
- 2010

### New set of symmetries of the integrable equations, Lie algebra and non-isospectral evolution equations. II: AKNS system

- Mathematics
- 1986

The authors define directly a new set of symmetries for the AKNS system and prove that they constitute an infinite-dimensional Lie algebra with the 'old' symmetries. They also point out the relation…

### Two Nonisospectral Integrable Hierarchies and its Integrable Coupling

- Mathematics, Physics
- 2020

In this paper we deduce two nonisospectral integrable hierarchies based on a Lie algebra F . To generating two expanding nonisospectral integrable hierarchies of the nonisospectral hierarchy, we…

### Three kinds of coupling integrable couplings of the Korteweg–de Vries hierarchy of evolution equations

- Mathematics
- 2010

We introduce three kinds of column-vector Lie algebras Ls(s=1,2,3). By making invertible linear transformations we get the corresponding three induced Lie algebras. According to the defined loop…

### Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV

- Mathematics
- 1991

We study a certain family of Schrödinger operators whose eigenfunctions ϕ(χ, λ) satisfy a differential equation in the spectral parameter λ of the formB(λ,∂λ)ϕ=Θ(x)ϕ. We show that the flows of a…