Abstract
Several new hierarchies of completely integrable systems, together with their respective hereditary recursion operators are given. Systematic methods for the construction of coupled completely integrable systems are developed. It is shown that — for most systems — a change of variable for the evolution parameter is compatible with complete integrability, bi-Hamiltonian structure and action-angle variable representation. A Lorentz-invariant recursion operator for the sine-Gordon equation is constructed.
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