Domain walls and vortices in two-mode photonic systems

We investigate 1D and 2D domain-wall (DW) states in systems of two nonlinear-Schrödinger (NLS) equations, which are coupled by the linear mixing and by the XPM (cross-phase-modulation). The system applies to the bimodal light propagation in nonlinear optics and two-component Bose-Einstein condensates. Approximate analytical solutions for the DWs are found near the point of the symmetry-breaking bifurcation of the CW (continuous-wave) states. An exact DW solution is obtained for ratio 3 : 1 of the XPM and SPM coefficients. The DWs between flat asymmetric CW states, which are mirror images to each other, are stable, while all other species of the DWs, with zero crossing(s) in one or two components, are unstable. An effective potential of attraction between DWs is derived. An exact stable solution is also found for the DW trapped by an external single-peak potential. In the 2D geometry, stable two-component vortices are found, with topological charges s = 1, 2, 3. Radial oscillations of annular DW-shaped pulsons, with s = 0, 1, 2, are studied too.