Vortex soliton in (2+1)-dimensional $$\mathcal {PT}$$ PT -symmetric nonlinear couplers with gain and loss

Abstract

We study the coupled nonlinear Schrodinger equation in the (2+1)-dimensional inhomogeneous \(\mathcal {PT}\)-symmetric nonlinear couplers and obtain \(\mathcal {PT}\)-symmetric and \(\mathcal {PT}\)-antisymmetric vortex soliton solutions. The dynamical behaviors of the completely localized structures (vortex solitons) are analytically and numerically investigated in a diffraction decreasing system with exponential profile. Numerical results indicate that one vortex soliton with different topological charges can stably propagate a long distance. The space between two humps and the modulation depth of vortex solitons add when the topological charge increases. However, the change tendency of the amplitude and width of vortex solitons is same with the increase in topological charge.