INTEGRABLE COUPLINGS AND BI-HAMILTONIAN STRUCTURES OF GENERALIZED ISOSPECTRAL-NONISOSPECTRAL C-KDV HIERARCHIES

Haiming Zong; Zhenbo Wang; Yufeng Zhang

doi:10.11948/20250130

2026 Volume 16 Issue 3

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Haiming Zong, Zhenbo Wang, Yufeng Zhang. INTEGRABLE COUPLINGS AND BI-HAMILTONIAN STRUCTURES OF GENERALIZED ISOSPECTRAL-NONISOSPECTRAL C-KDV HIERARCHIES[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1367-1400. doi: 10.11948/20250130

Citation:

Haiming Zong, Zhenbo Wang, Yufeng Zhang. INTEGRABLE COUPLINGS AND BI-HAMILTONIAN STRUCTURES OF GENERALIZED ISOSPECTRAL-NONISOSPECTRAL C-KDV HIERARCHIES[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1367-1400. doi: 10.11948/20250130

INTEGRABLE COUPLINGS AND BI-HAMILTONIAN STRUCTURES OF GENERALIZED ISOSPECTRAL-NONISOSPECTRAL C-KDV HIERARCHIES

1.
Research Office, Yantai Nanshan University, Yantai, Shandong 265700, China
2.
School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Author Bio: Email: zonghaiming@nanshan.edu.cn(H. Zong); Email: zyfusf@163.com(Y. Zhang)
Corresponding author: Email: wangzhenbocumt@163.com(Z. Wang)

Abstract

Abstract

In this paper, we derive a combined isospectral-nonisospectral C-KdV hierarchy, which generates some physically significant equations such as the generalized variable-coefficient C-KdV and Burgers equations. For the nonisospectral C-KdV equation, we establish infinite conservation laws and analyze invariant solutions and point symmetries for both the Burgers equation and the classical C-KdV equation. A key contribution is the construction of a new $ 4\times 4 $ Lie algebra $ g $ which enables the formulation of two linear problems. Their compatibility conditions yield isospectral and nonisospectral C-KdV integrable couplings. Using the quadratic-form identity, we derive the bi-Hamiltonian structures for the isospectral hierarchy, while the component-trace identity provides bi-Hamiltonian structures for the nonisospectral hierarchy.
- Isospectral and nonisospectral integrable hierarchy /
- bi-Hamiltonian structures /
- Lie algebra /
- conserved quantities /
- invariant solutions
MSC: 37K05, 37K40, 35Q53

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References

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