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

Amitava Choudhuri·B. Talukdar·S. B. Datta
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Abstract

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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Amitava Choudhuri, B. Talukdar, S. B. Datta. 2006-03-17. On a Generalized Fifth-Order Integrable Evolution Equation and its Hierarchy. https://doi.org/10.1515/zna-2006-1-202

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