Inverse scattering variables of the KdV equation from the point of view of Galilean mechanics

Publisher Website
Google Scholar
Abstract
The Galilean invariance of the Korteweg–de Vries equation is applied in order to characterize the structure of degrees of freedom displayed by the inverse scattering transform method. It is found that the dynamical systems associated with the discrete scattering data variables admit a description in terms of mass, position, and momentum variables similar to the systems of free Galilean particles. On the other hand, the radiation component of the KdV field associated with the continuous part of the set of scattering data turns out to be described by a new field evolving according to a linear partial differential equation.