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Inverse variational problem and canonical structure of Burgers equations. (English) Zbl 1067.37084
Summary: 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.

MSC:
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
35Q53 KdV equations (Korteweg-de Vries equations)
35R30 Inverse problems for PDEs
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