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.
Tefera et al. (Fri,) studied this question.