Galilean symmetry of the KdV hierarchy

Abstract By solving the infinitesimal Galilean symmetry for the Korteweg–de Vries (KdV) hierarchy, we obtain an explicit expression for the corresponding one‐parameter Lie group, which we call the Galilean symmetry of the KdV hierarchy. As an application, we establish an explicit relationship between the non‐abelian Born–Infeld partition function and the generalized Brézin–Gross–Witten partition function .