Dispersive optical soliton solutions of the \((2 + 1)\)-dimensional cascaded system governing by coupled nonlinear Schrödinger equation with Kerr law nonlinearity in plasma

In this article, the Kudryashov \(R\) function approach is employed to derive solitary wave solutions of a \((2 + 1)\)-dimensional cascaded system governed by coupled nonlinear Schrödinger equation with Kerr law nonlinearity using the travelling wave transformation. The method has various features that make symbolic computation much easier, especially when dealing with highly dispersive nonlinear equations. The approach has the advantage of not requiring the usage of a specific function form in computations. The method is especially useful for obtaining exact soliton solutions to nonlinear differential equations of higher order that explain pulse propagation in an optical fibre. The method provides an efficient, easy, and simple procedure for finding solitary wave solutions. Bright and singular soliton solutions have been extracted from the governing equation using this approach, which may be beneficial in various optoelectronic devices such as solar cells, blue lasers, optical couplers, LED traffic lights, photodiodes and magneto-optic waveguides. In order to illustrate the physical significance of the acquired solutions and by giving particular values to undefined parameters, the physical meaning of 3D and 2D geometrical structures for certain derived solutions has been shown here.