Optical solitons of the (2+1)-dimensional nonlinear Schrödinger equation with spatio-temporal dispersion in quadratic-cubic media

Abstract The major objective of this paper is to study the perturbed nonlinear Schrödinger equation with spatio-temporal dispersion in (2+1)-dimensional by using the complete discrimination system for polynomial. This paper discusses the propagation patterns in nonlinear fibers with quadratic-cubic nonlinearity. Additionally, a host of optical wave solutions are obtained, where solitary wave patterns and elliptic functions double periodic patterns are newly received. Besides, some two dimensional figures of solutions are illustrated in parameter space. All these solutions and figures are available to investigate the propagation dynamics of optical solitons in optical fibers.