Evolution of Radiative Initial Data in Higher-Order Nonlinear Schrödinger Equations: Stability Study

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DOI: https://doi.org/10.28924/2291-8639-23-2025-251
Published: Oct 16, 2025
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Umar Muhammad Dauda, Diaa S. Metwally, Sani Saleh Musa, Auwal Lawan, H. E. Semary, Mohammed Elgarhy, Evolution of Radiative Initial Data in Higher-Order Nonlinear Schrödinger Equations: Stability Study, Int. J. Anal. Appl., 23 (2025), 251.

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Umar Muhammad Dauda, Diaa S. Metwally, Sani Saleh Musa, Auwal Lawan, H. E. Semary, Mohammed Elgarhy

Abstract

This article presents a comprehensive numerical investigation of the fourth-order Schrödinger equation (FSE), a dispersive partial differential equation characterized by higher-order linear terms and nonlinear interactions for a localized and radiative initial data. Using the Implicit-Explicit (IMEX) splitting method, we address the computational challenges posed by the equation, balancing efficiency and stability for both localized and radiative initial data. We analyze the effects of dispersive parameters (β and γ) and nonlinear growth parameters (α and q) on the boundedness of the solutions. A dynamic framework is proposed to track stability using Sobolev norms and energy functionals. The numerical schemes are implemented with Fourier spectral methods for spatial discretization and Runge-Kutta schemes for time evolution. Our results demonstrate the efficacy of the IMEX splitting method in handling stiff dispersive terms while providing insights into parameter sensitivity. In addition, radiative initial data evolves into a decomposed smaller wave-packets.

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