Mathematics, General Mathematics, Applied Mathematics, Computational Mathematics
7
Scopus Publications
26
Scholar Citations
3
Scholar h-index
1
Scholar i10-index
Scopus Publications
Novel Soliton and Periodic Wave Solutions of the (3+1)-Dimensional Shallow Water Wave Equation with Bifurcation Analysis Wafy M. Hasan, Hamdy M. Ahmed, Ahmed M. Ahmed, Haytham M. Rezk, Wafaa B. Rabie Scientific Reports, 2025 This study derives novel exact traveling wave solutions for the $$(3 + 1)-$$ dimensional shallow water wave equation–a pivotal model in coastal hydrodynamics for tsunami prediction and tidal analysis. By employing an enhanced tanh-function method, we obtain a diverse spectrum of solutions, including dark, singular, and periodic solitons, as well as hyperbolic, Jacobi elliptic, rational, and exponential forms, which surpass the variety and generality reported in previous studies. These solutions uncover previously unexplored wave propagation patterns and interaction dynamics. A comprehensive bifurcation analysis elucidates the stability and phase transitions of the wave solutions, providing deeper analytical insight into their behavior. High-resolution graphical visualizations quantitatively demonstrate wave amplification and nonlinear interactions, confirming the superiority of our method in capturing complex physical phenomena. The results not only advance nonlinear wave theory but also enhance predictive models for marine hazard prevention and environmental monitoring strategies.
Exploring highly dispersive optical solitons and modulation instability in nonlinear Schrödinger equations with nonlocal self phase modulation and polarization dispersion Wafy M. Hasan, Hamdy M. Ahmed, Ahmed M. Ahmed, Haytham M. Rezk, Wafaa B. Rabie Scientific Reports, 2025 This study explores the dynamics of highly dispersive optical solitons in nonlinear Schrödinger equations (NLSE) with non-local self-phase modulation (SPM) and polarization-mode dispersion (PMD). These nonlinear effects significantly influence soliton propagation and stability in advanced optical communication systems. Employing the Improved Modified Extended Tanh-Function Method (IMETFM), we derive exact soliton solutions, including bright, dark, singular, and combo solitons, under specific parametric conditions. The IMETFM effectively handles the complexity of the NLSE, incorporating higher-order dispersion terms (up to sixth-order) and non-local nonlinearities. Additionally, we perform a modulation instability (MI) analysis to examine the stability of steady-state solutions. This analysis uncovers the conditions under which instabilities emerge due to the interplay between dispersion and nonlinearity. The MI study offers critical insights into the growth of wave perturbations, thereby advancing the understanding of soliton stability dynamics. Graphical representations of the solutions illustrate their behavior, emphasizing the impact of non-local SPM, PMD, and MI on soliton dynamics. These findings offer valuable insights for optimizing high-capacity optical communication systems and fiber laser technologies, with broader implications for nonlinear wave phenomena in birefringent fibers and other nonlinear physical systems. This work advances the theoretical framework for soliton dynamics and lays a foundation for future experimental validations and practical applications in nonlinear optics.
Perspectives on Dynamic Hardy–Littlewood Inequalities in Time Scale Analysis Taher S. Hassan, Wafy M. Hasan, Ioan-Lucian Popa, Mouataz Billah Mesmouli, Akbar Ali, et al. Mathematics, 2025 This study demonstrates several novel dynamic inequalities of the Hardy and Littlewood types on time scales. As special cases, our studies include Hardy’s integral inequalities and Hardy and Littlewood’s discrete inequalities. The research findings are demonstrated using algebraic inequalities, Hölder’s inequality, and the chain rule on time scales.
Construction of new travelling wave solutions and bifurcation analysis for the (2+ 1)-dimensional extended KP-BO equation utilizing the improved modified extended tanh-function … WM Hasan, WB Rabie, AM Ahmed, HM Rezk, HM Ahmed International Journal of Computer Mathematics 102 (12), 2214-2227 , 2025 2025 Citations: 6
Novel Soliton and Periodic Wave Solutions of the (3+ 1)-Dimensional Shallow Water Wave Equation with Bifurcation Analysis WM Hasan, HM Ahmed, AM Ahmed, HM Rezk, WB Rabie Scientific Reports 15 (1), 36490 , 2025 2025 Citations: 2
Exploring highly dispersive optical solitons and modulation instability in nonlinear Schrödinger equations with nonlocal self phase modulation and polarization dispersion WM Hasan, HM Ahmed, AM Ahmed, HM Rezk, WB Rabie Scientific Reports 15 (1), 27070 , 2025 2025 Citations: 6
Perspectives on Dynamic Hardy–Littlewood Inequalities in Time Scale Analysis TS Hassan, WM Hasan, IL Popa, MB Mesmouli, A Ali, HM Rezk Mathematics 13 (13), 2176 , 2025 2025
Dynamic Hardy-type inequalities with convex and non-convex functions on time scales HM Rezk, HM El-Owaidy, WM Hasan, AA El-Deeb Journal of Mathematical Sciences 290 (1), 87-102 , 2025 2025 Citations: 2
Generalizations of integral inequalities similar to Hardy in-equality on time scales WM Hasan, HM El-Owaidy, AA El-Deeb, HM Rezk Journal of Mathematics and Computer Science 32 (3), 241–256 , 2024 2024
A generalization of some integral inequalities similar to Hardy inequality on time scales WM Hasan, HM El-Owaidy, AA El-Deeb, HM Rezk Kuwait Journal of Science 51 (1), 100124 , 2023 2023 Citations: 10
MOST CITED SCHOLAR PUBLICATIONS
A generalization of some integral inequalities similar to Hardy inequality on time scales WM Hasan, HM El-Owaidy, AA El-Deeb, HM Rezk Kuwait Journal of Science 51 (1), 100124 , 2023 2023 Citations: 10
Construction of new travelling wave solutions and bifurcation analysis for the (2+ 1)-dimensional extended KP-BO equation utilizing the improved modified extended tanh-function … WM Hasan, WB Rabie, AM Ahmed, HM Rezk, HM Ahmed International Journal of Computer Mathematics 102 (12), 2214-2227 , 2025 2025 Citations: 6
Exploring highly dispersive optical solitons and modulation instability in nonlinear Schrödinger equations with nonlocal self phase modulation and polarization dispersion WM Hasan, HM Ahmed, AM Ahmed, HM Rezk, WB Rabie Scientific Reports 15 (1), 27070 , 2025 2025 Citations: 6
Novel Soliton and Periodic Wave Solutions of the (3+ 1)-Dimensional Shallow Water Wave Equation with Bifurcation Analysis WM Hasan, HM Ahmed, AM Ahmed, HM Rezk, WB Rabie Scientific Reports 15 (1), 36490 , 2025 2025 Citations: 2
Dynamic Hardy-type inequalities with convex and non-convex functions on time scales HM Rezk, HM El-Owaidy, WM Hasan, AA El-Deeb Journal of Mathematical Sciences 290 (1), 87-102 , 2025 2025 Citations: 2
Perspectives on Dynamic Hardy–Littlewood Inequalities in Time Scale Analysis TS Hassan, WM Hasan, IL Popa, MB Mesmouli, A Ali, HM Rezk Mathematics 13 (13), 2176 , 2025 2025
Generalizations of integral inequalities similar to Hardy in-equality on time scales WM Hasan, HM El-Owaidy, AA El-Deeb, HM Rezk Journal of Mathematics and Computer Science 32 (3), 241–256 , 2024 2024
