Published source of the Moser transformation

Ascertain whether Jürgen Moser’s published works explicitly contain the transformation defined in Definition 2.1 that maps the Neumann dynamical system variables (X,Y) to (U,V,W) via the generating polynomials U(ξ), V(ξ), and W(ξ) given in equations (2)–(4). If such a source exists, identify the precise publication and location; if not, clarify the attribution of this transformation.

Background

The paper builds a new integrable system—the Neumann–Moser dynamical system—by applying a transformation referred to as the Moser transformation to the complexified Neumann system. This transformation is central to several of the paper’s results, including explicit integrals, Lax representation, and connections to the KdV hierarchy.

David Mumford attributed this transformation to Jürgen Moser in his Tata Lectures on Theta II, but did not provide a citation. The authors note that despite searching, they could not find a place in Moser’s works where the transformation appears explicitly, creating a bibliographic uncertainty about its original source.