Formal recursion operators of integrable nonevolutionary equations and Lagrangian systems

Abstract

We derive the general structure of the space of formal recursion operators of nonevolutionary equations~$q_{tt}=f(q,q_x,q_t,q_{xx},q_{xt},q_{xxx},q_{xxxx})$. This allows us to classify integrable Lagrangian systems with a higher order Lagrangian of the form~$\mathcal{L}=\frac{1}{2}{L}_2(q_{xx},q_x,q)q_t^2+L_1(q_{xx},q_x,q)q_t+L_0(q_{xx},q_x,q)$. The key technique relays 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~$q_{tt}=f(q,q_x,\dots ,q_n;q_t,q_{xt},\dots ,q_{mt})$.

References in corpus (1)

• A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems