Investigation of exact soliton solutions in magneto-optic waveguides and its stability analysis

This paper deals the propagation of waves through magneto-optic waveguides which are modeled by the generalized vector nonlinear Schrodinger's equation (NLSE). Two types of nonlinearities namely quadratic-cubic (QC) and dual-power laws are studied by implementing authentic mathematical technique called extended Fan-sub equation (EFSE) method. We secure the exact solutions in the forms of Jacobi's elliptic functions, trigonometric, hyperbolic, including solitary wave solutions like bright, dark, complex, singular, and mixed complex solitons. Moreover, singular periodic wave solutions are recovered and the constraint conditions for valid soliton solutions are also reported. We also discuss the modulation instability (MI) analysis of the governing models. 3D and their corresponding 2D graphs are sketched for better understanding about the derived solutions with the values of unknown parameters. The most significant achievement of this approach is that it offers all the solutions that can be found by the use of other methods such as processes using the Riccati equation, an elliptic equation of the first kind, an auxiliary ordinary equation, or the generalized Riccati equation as mapping equation as well as we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied integration technique is concise, direct, efficient, and can be applied in more complex phenomena with the assistant of symbolic computations.

Automated summary

This paper examines the propagation of waves through magneto-optic waveguides using the generalized vector nonlinear Schrodinger's equation (NLSE). Two types of nonlinearities are studied, and exact solutions including various types of soliton solutions are obtained using the extended Fan-sub equation (EFSE) method. The significance of this approach lies in its ability to provide all solutions in a concise and efficient manner, as well as its applicability to more complex phenomena with symbolic computations.