Soliton dynamics of the Maccari model arising in plasma physics

Abstract

This paper develops some new solutions, along with trigonometric forms, Jacobi elliptic functions, and hyperbolic forms, for the Maccari system, arising in plasma physics, hydrodynamics, and nonlinear optics, applying the ${\phi }^6$-model expansion method. The 3D, contour, and 2D plots clearly show kink waves, breather waves, bright, dark, and singular periodic waves, and 2D overlapping phenomena. Additionally, the stability analysis of the obtained solution and bifurcation analysis of the system in question are also described. Our results show that the applied method is a promising tool for studying wave equations with nonlinear terms and for deepening our understanding of their dynamic complexity. The results of our research may improve the understanding of the Maccari system’s nonlinear dynamical features. This research ensures that the stated method is practical and compatible with the resolution of nonlinear problems. Our research not only enhances the mathematical resources but also models intricate wave phenomena in mathematical physics and advanced materials.