Formal recursion operators of integrable nonevolutionary equations and Lagrangian systems

Abstract

We derive the general structure of the space of formal recursion operators of integrable nonevolutionary equations qtt = f(q,qx,qt,qxx, . This allows us to classify integrable Lagrangian systems with a higher order Lagrangian of the form . The key technique relies on exploiting a homogeneity of the determining equations of formal recursion operators. This technique allows us to extend the main results to more general equations .