A New Completely Integrable Liouville's System Produced by the Ma Eigenvalue Problem

Abstract

Under the constraint between the potentials and eigenfunctions, the Ma eigenvalue problem is nonlinearized as a new completely integrablc Hamiltonian system (R^{2N}, dp∧dq, H): H = \frac{1}{2}α〈∧q,p〉 - \frac{1}{2}α_3 〈q,q〉 + \frac{α}{4α_3η} 〈q,p〉 〈p,p〉 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.