Dynamic Analysis of the (2+1)-Dimensional Zoomeron Model Using Advanced Analytical Techniques

In this paper, we investigate a nonlinear partial differential equation (NLPDE) known as the (2+1)-D Zoomeron model. This model is widely used in fluid dynamics, SONAR (Sound Navigation and Ranging) systems, optical fiber communication, and various other mathematical, physical, and technological fields. The exact solutions are obtained with the help of two advanced methodologies, the Sardar sub-equation technique and a new extended algebraic technique, that can offer a variety of soliton solutions with unique dynamic characteristics. These methodologies are efficient in understanding the complex behavior of the model. Traveling wave solutions are obtained in the paper with the help of Mathematica software, to explain a sound and effective new mathematical approach. The generated solutions cover a wide range of phenomena. These techniques give results in the form of plane wave solutions, hyperbolic solutions, periodic solutions, mixed periodic solutions, shock wave solutions, exponential solutions, and trigonometric solutions. Moreover, to understand the behavior of the obtained results, draw it in 3D, 2D as well, and contour from. The research outcomes increase the model’s accuracy and demonstrate the new concept’s value in learning technical physical systems. The next study in the domains of theoretical physics and applied mathematics is made possible by this work.