On Darboux transformations for soliton equations in high-dimensional spacetime

The Darboux transformations for a class of completely integrable systems in the spacetimeRn + 1, which are much more general than the systems inLett. Math. Phys.26, 199–209 (1989), are considered. The structure of the nonlinear evolution equations with space constraints is elucidated. It is pointed out that the inverse scattering method can be used to solve the Cauchy problem with initial data given on a noncharacteristic line.