The integrable systems associated with G.J. equation and its gauge equivalent Yang equation (Q917107)

The author discusses the hierarchy of partial differential equations based upon a generalization of the Ablowitz-Kaup-Newell-Segur hierarchy due to \textit{R. Giachetti} and \textit{R. Johnson}, Phys. Lett. 102A, 81-82 (1984)]. He generalizes further by the addition of a set of arbitrary functions of the independent variables and then specializes to hierarchies whose Hamiltonian structures are examined. The discussion is somewhat incomplete and the reader should consult \textit{F. Magri}, \textit{C. Morosi} and \textit{O. Ragnisco}, Commun. Math. Phys. 99, 115-140 (1985; Zbl 0602.58017). The author presents a one parameter family of integrable systems all having the same recursion operator. Finally he shows that a gauge transformation relates the Giachetti-Johnson equation to an equation of \textit{C. N. Yang} [Commun. Math. Phys. 112, 205-216 (1987; Zbl 0641.34024)]. In this formulation Yang hierarchy is not Hamiltonian.