Soliton Solutions for Coupled Nonlinear Generalized Zakharov Equations with Anti-cubic Nonlinearity Using Various Techniques

This study introduces novel exact solutions for the coupled nonlinear generalized Zakharov equations with anti-cubic nonlinearity. Utilizing a variety of mathematical approaches, including the extended trial function method, the rational exp (-ψ(ξ)) -expansion method, and three well-known auxiliary equation methods, a spectrum of solutions is derived. These solutions encompass dark solitons, bright solitons, singular solitons, Jacobi elliptic functions, periodic waves, and rational solutions. The unique contribution lies in the use of a phase variable θ(ξ) instead of a phase constant, providing fresh insights into wave behavior. A comparative analysis underscores the originality of the derived solutions, setting this work apart from prior studies. These findings advance our understanding of nonlinear dynamics and mathematical modeling, with potential applications in various domains.