THE NEUMANN–MOSER DYNAMICAL SYSTEM AND THE KORTEWEG–DE VRIES HIERARCHY

The paper’s chain of results is coherent: the Neumann–Moser ODEs (in generating-polynomial form) imply the t‑independent identity UξWξ+Vξ2, which yields constants of motion hk, a third‑order generating identity for U, and the Lenard recursion leading to an (n+1)-stationary KdV hierarchy; it also supplies a hyperelliptic Kleinian construction of solutions via Mumford’s system. These steps and statements appear correct (modulo a minor typo in the coordinate equation for ẇn+1). By contrast, the candidate solution’s Step 1 states an incorrect generating-series identity (it should be W−U = X(V̇+ΓU) in the X=ξ−1 chart, not W−XU = 1 + X(V̇−ΓU)), and it also flips the sign in the coefficient relation for wi+1. Although the candidate’s later conclusions match the paper after correcting these identities, the presented derivation as written is flawed.