The Formation and Propagation of Soliton Wave Profiles for the Shynaray-IIa Equation

This study examines a novel use of the Jacobi elliptic function expansion method to solve the Shynaray-IIA equation, a significant nonlinear partial differential equation that arises in optical fiber, plasma physics, surface symmetry geometry, and many other mathematical physics domains. This kind of solution has never been attained in research prior to this study. Numerous properties of a particular class of solutions, called the Jacobi elliptic functions, make them useful for the analytical solution of a wide range of nonlinear problems. Using this powerful method, we derive a set of exact solutions for the Shynaray-IIA equation, shedding light on its complex dynamics and behaviour. The proposed method is shown to be highly effective in obtaining exact solutions in terms of Jacobi elliptic functions, such as dark, bright, periodic, dark-bright, dark-periodic, bright periodic, singular, and other various types of solitons. Furthermore, a detailed analysis is conducted on the convergence and accuracy of the obtained solutions. The outcomes of this study extend the applicability of the Jacobi elliptic function approach to a novel class of non-linear models and provide valuable insights into the dynamics of Shynaray-IIA equation. This study advances the creation of efficient mathematical instruments for resolving intricate nonlinear phenomena across a range of scientific fields.