Non‐auto Darboux transformation for N$$ N $$‐soliton solutions of the non‐isospectral Korteweg–de Vries hierarchy

The usual non‐isospectral Korteweg–de Vries (KdV) hierarchy (see Equation 4) does not have auto Darboux transformations. In this paper, we present a non‐auto Darboux transformation for this hierarchy, from which we are able to construct its ‐soliton solutions. An explicit formula of the solutions with zero background is given, and solutions are illustrated.