Integrable Couplings and Bi-hamiltonian Structures of Generalized Isospectral-nonisospectral C-kdv Hierarchies
Year: 2025
Type: article
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.
DOI: 10.11948/20250130
Authors: Haiming Zong, Zhenbo Wang, Yufeng Zhang
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7117138182