Linearisation of Universal Field Equations
  The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the conjecture that these equations describe integrable systems. While this construction is implicit in general, there exists a large class of solutions for which an explicit form may be written. 
David B. Fairlie and Jan Govaerts