Tri-integrable couplings of the KdV hierarchy associated with a non-semisimple Lie algebra

Wen-Xiu Ma

Abstract


We explore the possibility of creating non-semisimple matrix loop algebras which lead to tri-integrable couplings containing two known integrable couplings. A semi-direct sum of Lie algebras consisting of specific $4\times 4$ block matrices is found to form the base of such integrable couplings. An application to the KdV equations is made as an illustrative example, and the resulting tri-integrable couplings are proved to possess bi-Hamiltonian structures, which
implies that there are infinitely many common commuting symmetries and conserved functionals determined by a hereditary recursion operator.

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References


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