https://doi.org/10.1140/epjp/s13360-024-05662-6
Regular Article
Exact solitary wave solutions and their comparisons under the effect of noise: an allelopathic phytoplankton competition model
1
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
2
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3
Department of Academic Affairs, School of Leadership and Business, Oryx Universal College With Liverpool John Moores University (UK), 12253, Doha, Qatar
4
Department of Humanities & Basic Sciences, Military College of Signals, National University of Science and Technology, Islamabad, Pakistan
5
MEU Research Unit, Faculty of Information Technology, Middle East University, Amman, Jordan
6
Department of Mathematics, University of Narowal, Narowal, Pakistan
Received:
17
March
2024
Accepted:
14
September
2024
Published online:
8
October
2024
In this study, we investigated an allelopathic phytoplankton competition model under the effect of Brownian motion. This model is analyzed for the first time analytically to obtain the solitary wave solution, numerical results, and mainly their comparisons. The solitary wave solutions are constructed by using the 
-model expansion method under the effects of noise. This approach provides us the Jacobi elliptic function solutions which form the two types of solutions such as soliton solution when we choose 
and solitary wave solutions when we choose 
. The different types of dark, bright, mixed, periodic, and periodic mixed solutions are gained under noisy environments. Moreover, the stochastic non-standard finite difference scheme is constructed for the approximate results. In addition, the proposed scheme is analyzed by providing consistency and stability of the scheme. The consistency is investigated under the mean square sense while the stability condition is gained with the help of Von-Neumann criteria. To show the physical behaviors of some solitons and solitary wave solutions, they are drawn in 3D and 2D form under the different effects of noise. Mainly, we are focusing on the comparison of the solitary wave results with the computational NSFD scheme via simulations. Some test problems are constructed from the newly constructed soliton solutions and compare the results in 3D and line plots.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
