Complete Integrability of General Nonlinear DifferentialDifference Equations Solvable by the Inverse Method. I
Abstract
General nonlinear differentialdifference equations of evolution which have been solved by the inverse method associated with a linear eigenvalue equationsqrt{a_{n + 1}}u_{n + 1} + sqrt{a_{n}}u_{n  1} = λ u_{n}are shown to describe completely integrable Hamiltonian systems. To this class belong the equation for Volterra system and the discretized KdV equation and others.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 October 1978
 DOI:
 10.1143/PTP.60.975
 Bibcode:
 1978PThPh..60..975K