article · Physica Scripta
This research investigates the perturbed higher-order modified Gerdjikov-Ivanov equation incorporating multiplicative white noise in the Ito interpretation. By applying the improved modified extended tanh-function method, an array of exact analytical solutions is derived. These encompass bright and dark solitons, singular and singular periodic solutions, hyperbolic wave solutions, rational functions, exponential functions, Weierstrass elliptic doubly periodic solutions, and Jacobi elliptic functions. The study specifically focuses on how white noise influences wave phenomena, demonstrating that the noise primarily acts upon the phase component of the resulting solitons. These solutions represent the first optical soliton derivations for this governing equation under the effect of multiplicative white noise, extending theoretical knowledge of wave behaviour within nonlinear optical systems.
Understanding how noise impacts wave stability and propagation is essential when modelling complex nonlinear systems. By discovering exact mathematical solutions that describe optical solitons in the presence of random fluctuations, this work helps researchers predict how wave signals behave under realistic, noisy operating conditions in optical environments.
The abstract does not indicate a direct commercial application pathway, as it represents early-stage mathematical and theoretical physics research. The derived solutions could eventually inform researchers and engineers modelling wave propagation in nonlinear optical systems where noise is present, but substantial applied testing and experimental development would be necessary before any practical use is feasible.
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Abstract The multiplicative white noise in the Ito interpretation is included for the first time in the perturbed higher-order modified Gerdjikov–Ivanov (HMGI) equation, that is considered the focus of the current study. In this work, we investigate the suggested model using the improved modified extended tanh-function (IMETF) method with the goal of producing brilliant and unique solitons such as dark and bright solitons, singular and singular periodic solutions, hyperbolic wave solutions, Weierstrass elliptic doubly periodic solutions, rational, exponential function solutions and Jacobi elliptic functions (JEFs). These extracted solutions demonstrate the effectiveness and potency of the used methodology. The used method specifies our research objective, which is related to solitons. These obtained soliton solutions are useful resources for examining a range of phenomena when there is white noise present. We examine how various wave phenomena are affected by noise, with a special emphasis on soliton solutions. Our findings indicate that the phase component for the obtained solitons of the suggested governing model is the primary goal of the white noise. This study is the first to show the optical soliton solutions derived from the perturbed HMGI equation under multiplicative white noise influence. The contribution of our work is the application of this phenomenon to a model equation in a new context that neither has been studied nor discovered before for optical soliton solutions. With the derived findings, our knowledge of wave events in nonlinear optical systems has advanced significantly.
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DOI: 10.1088/1402-4896/ada321
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