Baseband modulational instability and interacting localized mixed waves in coherently coupled optical media

Abstract

We consider a coherently coupled nonlinear Schrödinger equations (model equations) that describe interacting localized waves in coherently coupled optical media. The baseband modulational instability in such regimes is investigated, leading the result that the modulational instability does not necessary imply the baseband modulational instability. By means of a set of linear transformations, the model equations are converted into two independent scalar nonlinear Schrödinger equations. Based on the generalized perturbation (n,N−n)–fold Darboux transformation, we report and discuss analytical mixed localized wave solutions of these scalar equations. A first-order rogue wave solution of the scalar nonlinear Schrödinger equations is also presented. We then show that linear superpositions of different found analytical mixed localized wave solutions of the derived scalar equations results into several kinds of coherent nonlinear mixed structures such as, coexisting brigth/dark soliton-breather, rogue wave-breather-soliton, interacting rogue waves, bright/dark breathers, and bright/dark solitons.