Soliton solutions for the nonlinear Zoomeron equation applying the modified Khater method

This paper explores the nonlinear Zoomeron equation that is much used in the modeling of nonlinear wave propagation processes in several physical systems including fluid dynamics and nonlinear optics. The great nonlinearity of this equation renders search of analytical solutions to this equation to be a hard and significant problem. In order to solve this, the governing nonlinear partial differential equation is converted into an ordinary differential equation through the use of the modified Khater method (MKM) and its exact solutions are then built. In this method, a vast variety of new analytical solutions are discovered, including kink, anti-kink, singular periodic and dark solitary wave solutions. These solutions are further illustrated using the dynamical behavior by two-dimensional, three-dimensional and contour plots in mathematica. The results obtained prove that the Modified Khater method is a good and valid tool of analysis in solving nonlinear evolution equations. Additionally, the derived solutions add to the solution space of the Zoomeron model and give further insight into the complex nonlinear wave dynamics, which can be helpful in future theoretical and practical research.