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

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.