Exploring Advanced Soliton Solutions for the Stochastic Nonlinear System With Temporal Fractionality: Multiplicative Noise Intensity, Modulation Instability, and Chaotic Nature

Md. Mamunur Roshid, Ramy M. Hafez, Mahtab Uddin, Yakup Yildirim and Golam Mostafa

Journal of Applied Mathematics, 2026, vol. 2026, 1-14

Abstract: This study investigates the stochastic fractional new coupled Konno–Oono equation with external forced multiplicative noise, focusing on the chaotic nature, the influence of multiplicative noise intensity, and the fractionality parameter on exact soliton solutions. The proposed model is used to describe the complex phenomena in the magnetic field. To examine the exact solutions for the stochastic fractional new coupled Konno–Oono equation, the functional transformation method is applied. This method yields various forms of travelling wave solutions, including Jacobian elliptic, exponential, hyperbolic, and trigonometric functions, each dependent on different parameters. Additionally, we investigate the quasiperiodic and chaotic behavior of the system, including the formation of shock wave structures and sensitivity to initial conditions. The modulation instability is also investigated for the proposed model, which is important for quickly creating localized structures (such as solitons or rogue waves) by destabilizing unbroken waves when they are slightly disturbed, allowing for energy localization and spectrum widening. The findings in this study not only broaden but also enhance certain results from earlier research. Moreover, the influence of multiplicative noise on the analytical solutions of the stochastic system is illustrated through 3D diagrams and corresponding 2D path lines.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jam/2026/7600408.pdf (application/pdf)
http://downloads.hindawi.com/journals/jam/2026/7600408.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:7600408

DOI: 10.1155/jama/7600408

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().