On a Generalized Fifth-Order Integrable Evolution Equation and its Hierarchy

Details On a Generalized Fifth-Order Integrable Evolution Equation and its Hierarchy On a Generalized Fifth-Order Integrable Evolution Equation and its Hierarchy

2006-03-17

arxiv.org/abs/nlin/0603038v1

Z.Naturforsch 61a,page 7-15(2006)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, 1 figure

Scientific paper

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.

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