S.A. Bronsard and D.E. Pelinovsky

New integrable semi-discretizations of the coupled nonlinear Schr0dinger equations

Abstract:
We have undertaken an algorithmic search for new integrable semi-discretizations of physically relevant nonlinear partial differential equations. The search is performed by using a compatibility condition for the discrete Lax operators and symbolic computations. We have discovered a new integrable system of coupled nonlinear Schrodinger equations which combines elements of the Ablowitz-Ladik lattice and the triangular-lattice ribbon studied by Vakhnenko. We show that the continuum limit of the new integrable system is given by uncoupled complex modified Korteweg-de Vries equations and uncoupled nonlinear Schrodinger equations.

Keywords:
integrable systems, Lax pairs, semi-discretizations, Ablowitz-Ladik lattice, triangular-lattice ribbon, coupled nonlinear Schrodinger equations