New Optical Dromion and Domain Wall Solutions of Cascaded System in $$(2+1)$$ ( 2 + 1 ) -Dimensions Via Various Analytical Architectures

In this paper, we applied the generalized exponential rational function method, the new modified sub-ODE method, the new extended auxiliary equation method, the new Jacobi elliptic function expansion method, and the direct Jacobi elliptic function method to study the (2+1)-dimensional coupled nonlinear Schrödinger equation with cascading effect. As an outcome, the kink-antikink, singular, and non-singular bright dromion, the domain wall solutions, the Weierstrass elliptic function, the doubly periodic, and other optical wave solutions have thus emerged. Furthermore, essential conditions for the existence of the solutions are given. Despite their simplicity and ease of use, these techniques are very powerful and may be used to solve a wide range of problems. The results obtained may be helpful in understanding of wave propagation in optical couplers, birefringent fibers, and optoelectronic devices. The acquired results are compared to the well-known results in the literature. For appropriate parameter selections, the dynamical behavior of some of the obtained solutions is analyzed via 2D and 3D graphs.