Hollow ring-like soliton and dipole soliton in ( $$\varvec{2+1}$$ 2 + 1 )-dimensional $$\varvec{\mathcal {PT}}$$ PT -symmetric nonlinear couplers with gain and loss

Abstract

By means of the Hirota bilinear method, we obtain the hollow ring-like soliton and dipole soliton solutions of the coupled nonlinear Schrodinger equation in the ( $$2+1$$ )-dimensional inhomogeneous $${\mathcal {PT}}$$ -symmetric nonlinear couplers. Based on these analytical solutions, we investigate the compression behaviors of hollow ring-like soliton and dipole soliton in a diffraction decreasing system with exponential profile.