Bi-Integrable Couplings Associated with so $$(3,{\mathbb R})$$ ( 3 , R )

Abstract

By a class of zero curvature equations over a non-semisimple matrix loop algebra, we generate a new hierarchy of bi-integrable couplings for a soliton hierarchy associated with so(3, $$\mathbb {R}$$ ). The bi-Hamiltonian structures are found by the associated variational identity, which imply that all the presented coupling systems possess infinitely many commuting symmetries and conserved functionals and, thus, are Liouville integrable.