Diverse wave solutions for the (2+1)-dimensional Zoomeron equation using the modified extended direct algebraic approach

This work used the modified extended direct algebraic expansion method to find exact soliton solutions for the (2+1)-dimensional nonlinear Zoomeron equation. The modified extended direct algebraic technique employs a wave transformation and, in order to determine solutions, it then performs an algebraic expansion, compares coefficients, and balances the equation. The results were an effective acquisition of a variety of solitons with unique wave characteristics including bright, kink, periodic, singular periodic, and dark solitons. A stability investigation has confirmed the structural integrity of these solutions under minor perturbations. In the form of 2D, contour, and 3D graphical representations, the stability and propagation of these solutions were further investigated. The findings illustrate how effectively this technique can solve higher-dimensional nonlinear equations and yield more soliton solutions. Beyond broadening our knowledge of nonlinear wave behavior, this research could be beneficial in nonlinear optics, fluid motion, and plasma systems.