Soliton propagation under diffusive and nonlinear effects in physical systems; (1+1)–dimensional [formula omitted] integrable equation

Abstract

This study presents recent advancements in computational techniques for discovering new and precise solitary wave solutions in the (1 + 1)-dimensional Mikhailov-Novikov-Wang (MNW) integrable equation. Solitary wave solutions are crucial in understanding complex nonlinear phenomena and have practical applications in fields such as fluid dynamics, nonlinear optics, and plasma physics. The proposed computational techniques utilize powerful numerical methods, including the extended simplest equation (ESE) method, modified Riccati expansion MRE method, and He's variational iteration (HVI) method. These techniques provide robust and accurate ways to compute solitary wave solutions, taking advantage of the integrability properties of the MNW equation. Compared to traditional computational methods, these approaches offer significant improvements in efficiency, accuracy, and the ability to explore a broader range of solitary wave solutions. The study demonstrates the effectiveness of these techniques through extensive numerical simulations and comparisons with other computational approaches. The results highlight the superior performance of the proposed methods in identifying new solitary wave solutions, accurately characterizing their properties, and providing deeper insights into the behavior of the model. These computational techniques contribute to advancing our understanding of the underlying dynamics of the MNW equation and have potential applications across various scientific disciplines.