Stability of (1 + 1)-dimensional coupled nonlinear Schrödinger equation with elliptic potentials

Abstract

In this work, the (1 + 1)-dimensional coupled nonlinear Schrodinger equation with external elliptic potentials is studied. The exact expressions are obtained for spatially modulated periodic wave solutions in terms of Jacobi elliptic functions. The hyperbolic limits of these solutions are also considered. The cases of both attractive and repulsive nonlinear coefficients have been considered. The linear stability of these solutions is investigated both analytically and numerically. Different stable patterns, e.g., bright-bright and kink-kink solitons, are also obtained.