A fused hierarchy. (Q1853816)

The inverse scheme [see \textit{K. Imai}, \textit{K. Konno} and \textit{H. Kakuhata}, J. Phys. Soc. Japan 68, 1115--1120 (1999; Zbl 0942.37045)] is a powerful tool to discuss integrable systems. By using the scheme, one can study hierarchy structures of the scheme. Some schemes constitute two hierarchies. Usually, two hierarchies associated with the same eigenvalue problem are not connected, for example, the mKdV and sine-Gordon hierarchies. Here, the authors find that it is possible to look for other integrable hierarchies by examining the relation between the two recursion operators of the IKK system [see \textit{K. Konno}, \textit{K. Imai} and \textit{H. Kakuhata}, Phys. Lett., A 286, 47--54 (2001; Zbl 0969.37504)]. Based on the result, a scheme is presented from which two hierarchies of the IKK system are fused into a grand hierarchy.