Soliton solutions to a nonlinear wave equation via modern methods

In this pioneering study, we have systematically derived traveling wave solutions for the highly intricate Zoomeron equation, employing well-established mathematical frameworks, notably the modified (G′/G)-expansion technique. Twenty distinct mathematical solutions have been revealed, each distinguished by distinguishable characteristics in the domains of hyperbolic, trigonometric, and irrational expressions. Furthermore, we have used the formidable computational capabilities of Maple software to construct depictions of these solutions, both in two-dimensional and three-dimensional visualizations. The visual representations vividly capture the essence of our findings, showcasing a diverse spectrum of wave profiles, including the kink-type shape, soliton solutions, bell-shaped waveforms, and periodic traveling wave profiles, all of which are clarified with careful precision.