Analytical optical solutions to the nonlinear Zakharov system via logarithmic transformation

Abstract

In the past few years, there has been a growing interest in investigating the search for solitary wave solutions in the realm of nonlinear partial differential equations. This endeavor represents a captivating and challenging area of research. The primary objective of this study is to investigate the nonlinear Zakharov system through a comprehensive analysis that integrates logarithmic transformations and the symbolic structures of exponential functions. The nonlinear Zakharov system holds remarkable importance as a fundamental cornerstone in the field of plasma physics, derived from the profound intellect of esteemed mathematicians and physicists. By examining a diverse range of solution forms including trigonometric, hyperbolic, and rational expressions, this research delves into the complexities of plasma behavior. Notably, the introduction of arbitrarily selected constants imbues these solutions with a multifaceted and dynamic nature. In support of the findings, the article presents several numerical simulations that align with the derived solutions. The utilized methods stand out for being simple, reliable, and capableof creating fresh solutions for nonlinear partial differential equations in the realm of mathematical physics. Other significance of this research lies in its introduction of innovative methodologies previously unexplored in the study of this particular model, thereby broadening the scientific toolkit. Moreover, the versatility of these techniques offers the potential for seamless adaptation in addressing various other nonlinear partial differential equations.