Nonlinear discrete systems with nonanalytic dispersion relations

Abstract

A discrete system of coupled waves (with nonanalytic dispersion relation) is derived in the context of the spectral transform theory for the Ablowitz–Ladik spectral problem (discrete version of the Zakharov–Shabat system). This 3-wave evolution problem is a discrete version of the stimulated Raman scattering equations, and it is shown to be solvable for arbitrary boundary value of the two radiation fields and initial value of the medium state. The spectral transform is constructed on the basis of the ∂-approach.