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Published in last 50 years
The author discusses the behaviour of Hamiltonian structures for a generalised AKNS hierarchy under componentwise reductions to equations of KdV and MKdV type, identifying those cases where a new local structure arises.
A systematic exposition is given of recent results of the general algebraic theory of soliton equations with an elliptic sheaf which generalize a number of “integrable” two-dimensional matrix differential equations, starting with the equations of principal chiral fields. Local conservation laws, Bäcklund-Darboux transformations, algebra-geometric solutions, quantum integrals, and Hamiltonian structure are studied.