Non-Isospectral Korteweg-de Vries Equation from the Cauchy Matrix Approach
Abstract
This paper develops the Cauchy matrix approach to formulate the non-isospectral Korteweg-de Vries equation and derive its explicit soliton solutions. A Sylvester equation is employed to define a set of scalar functions \(\{ S^{(i,j)}\}\) . By introducing non- isospectral dispersion relations, the evolution equations for \(\{ S^{(i,j)}\}\) are systematically established. Several fundamental identities of these functions are utilized to verify the correctness of the obtained solutions. Moreover, explicit soliton solutions are presented, accompanied by a detailed analysis of their dynamical characteristics.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Advanced Mathematical Physics Problems
Numerical methods for differential equations
Publication details
- Journal / source
- Journal of Nonlinear Mathematical Physics
- Volume
- 33
- Issue
- 1
- Publication date
- 6 February 2026
- Language
- EN