A New Completely Integrable Liouville's System Produced by the Ma Eigenvalue Problem (Journal of Partial Differential Equations, 1997)
Under the constraint between the potentials and eigenfunctions, the Ma eigenvalue problem is nonlinearized as a new completely integrablc Hamiltonian system (R^{2N}, dp&#8743dq, H): H = \frac{1}{2}&#945&#9001&#8743q,p&#9002 - \frac{1}{2}&#945_3 &#9001q,q&#9002 + \frac{&#945}{4&#945_3&#951} &#9001q,p&#9002 &#9001p,p&#9002 The involutive solution of the high-order Ma equation is also presented. The new completely integrable Hamiltonian systems are obtained for DLW and Levi eigenvalue problems by reducing the remarkable Ma eigenvalue problem.