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

The nonlinear Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger 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.