Nonlinear differential−difference equations

Abstract

A method is presented which enables one to obtain and solve certain classes of nonlinear differential−difference equations. The introduction of a new discrete eigenvalue problem allows the exact solution of the self−dual network equations to be found by inverse scattering. The eigenvalue problem has as its singular limit the continuous eigenvalue equations of Zakharov and Shabat. Some interesting differences arise both in the scattering analysis and in the time dependence from previous work.