Investigating closed form soliton solutions to the Riemann wave equation by using two novel methods

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Okara, Okara, Pakistan.

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

3 Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, P.C. 44891-63157, Iran.

Abstract

The present work aims to investigate solitary wave solutions for the recently developed (2 + 1)-
dimensional Riemann wave equation, which is a signifcant mathematical model in nonlinear sciences with fascinating applications in fluid dynamics, optics, image processing, plasma physics
etc. To analyze this model, we employ a novel modifed Sardar sub-equation method and new
Kudryashov’s method to generate several sorts of soliton solutions. A range of categories are
encompassed by these solutions, such as periodic, bright solitons, singular solitons, dark solitons,
combo bright-singular solitons, exponential, and rational solutions. To highlight the dynamic
behavior and physical importance of the optical soliton solutions of proposed model, several
graphical simulations, by three-dimensional (3D) graphs and two-dimensional (2D) plots, are
used. This work suggests a major advancement in comprehending the intricate and unpredictable behavior of this model, encouraging readers to explore the world of nonlinear waves
and dynamic systems.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 14 December 2025

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History

  • Receive Date: 23 July 2024
  • Revise Date: 28 October 2025
  • Accept Date: 08 December 2025

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