Euler–Poincaré Formalism of KDV–Burgers and Higher Order Nonlinear Schrodinger Equations

In this paper we derive the KdV–Burgers and higher order nonlinear Schrodinger equations as an Euler–Poincaré flow on the joint space of Hill's and first order differential operators on circle. We also study a quasi-hamiltonian pair of involution equations one member of which is the KdV–Burger equation.