Extension of the perturbation-iteration method to (1+2)-dimensional case

Abstract By extending the (1+1)-dimensional [(1+1)-D] perturbation-iteration method suggested by Hong et al. [J. Opt. Soc. Am. B 35 (2018) 317-322] to the (1+2)-D case, we develop an arithmetic to the numerical integration for solition solutions of the (1+2)-D nonlocal nonlinear Schrodinger equation, and obtain the Gaussian-like solitons in Cartesian coordinate system and the Laguerre-Gaussian-type-like solitons in cylindrical coordinates system. Moreover, some more accurate soliton solutions were obtained through optimizing the calculation method of the nonlinear refractive index.