Integrable Hamiltonian equations of fifth order with the Hamiltonian operator $\boldsymbol D_x$

TL;DR

This paper classifies all non-equivalent fifth-order integrable evolution equations of a specific form involving a Hamiltonian operator, expanding understanding of integrable systems in mathematical physics.

Contribution

It systematically identifies all such fifth-order integrable equations with the Hamiltonian operator D_x, providing a comprehensive classification.

Findings

Complete list of fifth-order integrable equations of the specified form

Identification of non-equivalent equations within this class

Advancement in the theory of integrable Hamiltonian systems

Abstract

All non-equivalent integrable evolution equations of the fifth order of the form $u_t=D_x\frac{\delta H}{\delta u}$ are found.