DECOMPOSITION AND STRAIGHTENING OUT OF THE DISCRETE KAUP–NEWELL FLOWS

Abstract

A coupled 2+1-dimensional discrete Chen–Lee–Liu equation is proposed, which together with two 1+1-dimensional discrete Kaup–Newell equations is decomposed into solvable ordinary differential equations with the help of the resulting Lax matrix and its finite-order expansion. Based on the theory of the algebraic curve, the Abel–Jacobi coordinates are introduced to straighten out the corresponding continuous flow and discrete flow, by which explicit solutions for the coupled 2+1-dimensional discrete Chen–Lee–Liu equation and the 1+1-dimensional discrete Kaup–Newell equations are obtained in the Abel–Jacobi coordinates.