Soliton structures of the modified unstable nonlinear Schrödinger equation and their applications in nonlinear optical communication systems

Abdulhamed Alsisi; Rayan Hamza Alsisi; Abdulhamed Alsisi; Rayan Hamza Alsisi

doi:10.3934/math.2026560

AIMS Mathematics

2026, Volume 11, Issue 5: 13617-13631. doi: 10.3934/math.2026560

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Research article

Soliton structures of the modified unstable nonlinear Schrödinger equation and their applications in nonlinear optical communication systems

Abdulhamed Alsisi ¹,
Rayan Hamza Alsisi ^{2
,
,}

1.
Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia
2.
Department of Electrical Engineering, Faculty of Engineering, Islamic University of Madinah, Madinah, Saudi Arabia

Received: 05 March 2026 Revised: 13 April 2026 Accepted: 08 May 2026 Published: 15 May 2026
MSC : 35B40, 35C05, 35Q35, 35Q55

This work focuses on the modified unstable nonlinear Schrödinger equation. It is an important model for forecasting the evolution of unstable nonlinear wave packets in dispersive media. We derive several new solitary wave solutions, including periodic, dark, explosive, and singular waveforms, utilizing a new closed-form analytical technique. The proposed solutions demonstrate the complex interactions of wave amplitude, velocity, and localization with the system's nonlinear and dispersive properties, providing clear insight into instability causes. MATLAB is employed to generate two-dimensional, three-dimensional, and trajectory plots of the selected solutions, thereby facilitating the visualization of solitary wave propagation in the modified unstable nonlinear Schrödinger equation. This deeper analytical insight allows for better management of dispersion, nonlinearity, and instability evolution, resulting in increased transmission distance, spectrum efficiency, and signal robustness. Finally, the study demonstrates that accurately constructed soliton structures, formulated within the modified unstable framework, offer a robust and scalable approach for next-generation optical communication systems operating in highly nonlinear and ultrafast regimes.
- closed form framework,
- solitary waves,
- mUNLSE model,
- modern fiber-optic systems
Citation: Abdulhamed Alsisi, Rayan Hamza Alsisi. Soliton structures of the modified unstable nonlinear Schrödinger equation and their applications in nonlinear optical communication systems[J]. AIMS Mathematics, 2026, 11(5): 13617-13631. doi: 10.3934/math.2026560

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Abstract

This work focuses on the modified unstable nonlinear Schrödinger equation. It is an important model for forecasting the evolution of unstable nonlinear wave packets in dispersive media. We derive several new solitary wave solutions, including periodic, dark, explosive, and singular waveforms, utilizing a new closed-form analytical technique. The proposed solutions demonstrate the complex interactions of wave amplitude, velocity, and localization with the system's nonlinear and dispersive properties, providing clear insight into instability causes. MATLAB is employed to generate two-dimensional, three-dimensional, and trajectory plots of the selected solutions, thereby facilitating the visualization of solitary wave propagation in the modified unstable nonlinear Schrödinger equation. This deeper analytical insight allows for better management of dispersion, nonlinearity, and instability evolution, resulting in increased transmission distance, spectrum efficiency, and signal robustness. Finally, the study demonstrates that accurately constructed soliton structures, formulated within the modified unstable framework, offer a robust and scalable approach for next-generation optical communication systems operating in highly nonlinear and ultrafast regimes.

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