Inverse variational problem and canonical structure of Burgers equations

Abstract

It is demonstrated that Burgers equations, which are often believed to describe dissipative systems, are non-Lagrangian. Following Bateman’s analysis of damped harmonic oscillator an action is defined to look for a Lagrangian representation for equations in the Burgers hierarchy. The associated higher-order Lagrangian densities are found to be degenerate such that the Hamiltonian structure could be studied by a repackaging of Ostrogradski formalism and Dirac’s theory of constraints.