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 Diraca€?s theory of constraints. The speci???c results presented refer to the third- and ???fth-order equations of the so-called distinguished subclass.
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