Some new integrable systems of two-component fifth order equations

Abstract

In this work we develop some fifth-order integrable coupled systems of weight $0$ and $1$ which possess seventh-order symmetry. We establish four new systems, where in some cases, related recursion operator and bi-Hamiltonian formulations are given. We also investigate the integrability of the developed systems.

16 pages. This paper is merger of complete version of a draft with archive number arXiv:1305.4567 and some other possible new systems