New solitons and breather-like solutions to a (2+1)-dimensional coupled variable-coefficient Schrödinger equation in optical fibers

The nonlinear Schr & ouml;dinger equation is an important theoretical model for ultra-long and ultra-fast transportation. Therefore, the situation of its normal propagation and collision has significant implications for practical applications. For example, the nonlinear Schr & ouml;dinger models can be utilized in the optical, plasma and fluid dynamics fields. However, current researches mainly focus on solutions of one dimensional or two dimensional Schr & ouml;dinger equations with constant coefficients. Although these solutions possess good properties, they are often too unilateral. In this paper, our research mainly focuses on solutions of a (2+1)-dimensional coupled variable-coefficient Schr & ouml;dinger equation. Through an explicit transformation, the solutions of this equation in the form of one-soliton, two-soliton, three-soliton, and breather-like bright-dark solitons can be acquired by utilizing the developed Hirota bilinear method. Furthermore, we will explicate that the collisions among two-soliton, two-breather-like bright-dark soliton are elastic with the help of the asymptotic analysis method. At last, we will exhibit their collisions via illustrations.