Rogue waves and other solutions of single and coupled Ablowitz–Ladik and nonlinear Schrödinger equations

Abstract

We provide a simple technique for finding the correspondence between the solutions of Ablowitz–Ladik and nonlinear Schrodinger equations. Even though they belong to different classes, in that one is continuous and one is discrete, there are matching solutions. This fact allows us to discern common features and obtain solutions of the continuous equation from solutions of the discrete equation. We consider several examples. We provide tables, with selected solutions, which allow us to easily match the pairs of solutions. We show that our technique can be extended to the case of coupled Ablowitz–Ladik and nonlinear Schrodinger (i.e. Manakov) equations. We provide some new solutions.