A general form of the fifth-order nonlinear evolution equation is considered.
Helmholtz solution of the inverse variational problem is used to derive
conditions under which this equation admits an analytic representation. A
Lennard type recursion operator is then employed to construct a hierarchy of
Lagrangian equations. It is explicitly demonstrated that the constructed system
of equations has a Lax representation and two compatible Hamiltonian
structures. The homogeneous balance method is used to derive analytic soliton
solutions of the third- and fifth-order equations.Comment: 16 pages, 1 figur
