Symbiotic Rogons in (2+1)-Dimensional GRIN Waveguide

In this chapter, we propose variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE) as a model for the description of multimode wave propagation in inhomogeneously coupled nonlinear optical fibers. This dynamical system admits bright–dark, bright, dark similaritons, self-similar breathers, and rogue waves as possible localized configurations, under specific conditions on the self- and cross-phase coupling terms. By appropriately lowering the strength of the self-phase modulation in comparison to the cross-phase coupling terms, out of these solutions, one of the propagating modes can be made prominent. For the equal contributions of self- and cross-phase modulations, we show that this inhomogeneous system supports semi-rational self-similar rogue waves (rogons).