Dynamical characteristics and modulation instability (MI) analysis of sharp ‎slope bell soliton and kink wave solutions to the perturbed space-time fractional Boussinesq equation

Authors

  • Foyjonnesa Lecturer of Mathematics at Bangladesh Army University of Science and Technology
  • Jobayad Bhuiyan Lecturer of Mathematics at Bangladesh Army University of Science and Technology
  • Mst. Ummey Kulsum Assistant Professor of Mathematics at Bangladesh Army University of Science and Technology

How to Cite

Foyjonnesa, Bhuiyan, J., & Mst. Ummey Kulsum. (2025). Dynamical characteristics and modulation instability (MI) analysis of sharp ‎slope bell soliton and kink wave solutions to the perturbed space-time fractional Boussinesq equation. International Journal of Physical Research, 13(1), 1-11. https://doi.org/10.14419/sqp3vq09

Received date: March 25, 2025

Accepted date: April 14, 2025

Published date: May 8, 2025

DOI:

https://doi.org/10.14419/sqp3vq09

Keywords:

Space-Time Fractional Perturbed Boussinesq Equation; Conformable Derivative (CD); The Advanced- exp⁡(-ϕ(ξ)) Expansion Technique; Modulation Instability MI Analysis; Soliton Solutions

Abstract

To attain soliton results for the nonlinear fractional progression equations (NLFEEs) like the space-time fractional Boussinesq equation, we have utilized the advanced expansion technique. In this study, solutions are explicitly determined as kink, soliton, and sharp slope ‎bell soliton types. These obtained singular wave solutions might play a significant role in finding the mathematical model of the realistic corporal phenomena. The results illustrated that the advanced-  expansion technique is a simple, straightforward, and actual mathematical ‎model for searching extensive wave solutions with suitable parameters of higher-dimensional NLFEEs. We have also applied the modulation instability analysis (MI) to deliberate the consistency scrutiny of the achieved solutions, and the driving character of the obtained waves is ‎inspected, which ensures that all achieved solutions are explicit, reliable, exact, and stable‎.

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How to Cite

Foyjonnesa, Bhuiyan, J., & Mst. Ummey Kulsum. (2025). Dynamical characteristics and modulation instability (MI) analysis of sharp ‎slope bell soliton and kink wave solutions to the perturbed space-time fractional Boussinesq equation. International Journal of Physical Research, 13(1), 1-11. https://doi.org/10.14419/sqp3vq09

Received date: March 25, 2025

Accepted date: April 14, 2025

Published date: May 8, 2025