Solitary Wave Structures of the One-Dimensional Mikhailov-Novikov-Wang System Using Kudryashov's New Function Method

Abstract

Traveling waves and integrable equations are the most well-known features of nonlinear wave propagation phenomena. Analytical solutions to nonlinear integrable equations play an important role in examining the behaviour and structure of nonlinear systems. They offer valuable insights into how these systems evolve over time and under different conditions. Such solutions are essential for accurately describing a range of realworld phenomena. This study aims to derive closed-form traveling wave solutions of the (1+1)-dimensional Mikhailov-Novikov-Wang model by employing the Kudryashovʼs new function method. This system provides novel erspectives for understanding the connection between integrability and water wave phenomena. New solitary wave solutions are constructed in terms of hyperbolic functions by assigning particular values of the parameters. The study yields two types of solitons, including bell-shaped and singular soliton solutions. The solutions are simulated in 2D and 3D graphical representations to illustrate their physical features. The results highlight the effectiveness of the employed approach in constructing novel solutions which are essential to understand the dynamics of the governing system.