Isospectral problem for Schrodinger operator: Evolutional viewpoint

An isospectral transform of the Schrodinger operator is considered as an ev olutional problem. For a transform defined by the McKean-Trubowitz flows as sociated evolutional equations are derived. It is shown that for one-level and two-level flows these equations can be split into integrable Liouville equations. A relationship between the Liouville equations and the Darboux t ransforms is discussed; this analysis suggests that the evolutional equatio ns can be split into the Liouville equations in the general case. A Hamilto nian formulation of the isospectral transform defined by the McKean-Trubowi tz flows is presented. It is shown that this transform is performed by a ca nonical change of variables, which is related to the Darboux transform. (C) 1999 American Institute of Physics. [S0022-2488(99)02403-2].