Inverse problem of the variational calculus for higher KdV equations

Abstract:

It is shown that the usual Hamilton's variational principle supplemented by the methodology of the integer-programming problem can be used to construct expressions for the Lagrangian densities of higher KdV fields. This is demonstrated with special emphasis on the second and third members of the hierarchy. However, the method is general enough for applications to equations of any order. The expressions for Lagrangian densities are used to calculate results for Hamiltonian densities that characterize Zakharov-Faddeev-Gardner equation.