Gauge transformation between the first-order nonisospectral and isospectral Heisenberg hierarchies

By means of the Ablowitz-Kaup-Newell-Segur system with symbolic computation, the gauge transformation between the first-order nonisospectral and isospectral Heisenberg spectral problems is obtained. Correspondingly, the equivalence relation between the first-order nonisospectral and isospectral Heisenberg hierarchies is given. In addition, further applications and potential research directions of our method are discussed.