Gauge transformation and spectral decomposition for the Ishimori-II equations

We study the gauge transformation between spectral problems and their adjoints for the Ishimori-II (IS-II) and Davey–Stewartson-II (DS-II) equations. The commutativity between the gauge and adjoint transformations is proved. The commutativity is used for spectral decomposition and surface representation theorems for the Ishimori-II equations.