Canonical structure of evolution equations with non-linear dispersive terms

摘要

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. Keywords Evolution equations - non-linear dispersive terms - Lagrangian systems - Hamiltonian structure PACS Nos 47.20.Ky - 42.81.Dp