Canonical structure of evolution equations with non-linear dispersive terms
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The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The specific results presented refer to the third- and fifth-order equations of the so-called distinguished subclass.
KeywordsEvolution equations non-linear dispersive terms Lagrangian systems Hamiltonian structure
PACS Nos47.20.Ky 42.81.Dp
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