Publications

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2024
Abdel-Gawad, H. I., and M. A. El Mahdy, "Analytic solutions of alpha-beta-time-derivatives complex finance chaotic dynamical system: synchronization and extended center manifold. An explicit approach", Physica Scripta, vol. 99, no. 6: IOP Publishing, pp. 065203, 2024. Abstract
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Abdel-Gawad, H. I., T. A. Sulaiman, and H. F. Ismael, "Bright–dark envelope-optical solitons in space-time reverse generalized Fokas–Lenells equation: Modulated wave gain", Modern Physics Letters B: World Scientific Publishing Company, pp. 2450377, 2024. Abstract
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Abdel-Gawad, H. I., "Characteristics of velocity, bubble's radius, and pressure in liquid and gas bubble mixture", Physics of Fluids, vol. 36, no. 2: AIP Publishing, 2024. Abstract
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Tantawy, M., and H. I. Abdel-Gawad, "Dynamics of molecules in torsional DNA exposed to microwave and possible impact on its deformation: stability analysis", The European Physical Journal Plus, vol. 139, no. 4: Springer Berlin Heidelberg, pp. 1–17, 2024. Abstract
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Ibrahim, I. E., H. I. Abdel-Gawad, W. M. Moslem, and I. S. Elkamash, "The effect of Enceladus’s space debris on DAWs in Saturn’s E ring in the presence of suprathermal particles", Chinese Journal of Physics: Elsevier, 2024. Abstract
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Abdel-Gawad, H. I., B. Abd El-Aziz, and M. Tantawy, "EXTENDED CENTER MANIFOLD, GLOBAL BIFURCATION AND APPROXIMATE SOLUTIONS OF CHEN CHAOTIC DYNAMICAL SYSTEM", Journal of Applied Analysis & Computation, vol. 14, no. 4: Journal of Applied Analysis & Computation, pp. 2125–2139, 2024. Abstract
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Abdel-Gawad, H. I., and A. H. Abdel-gawad, "Mathematical analysis of the new $\alpha$-difference operator with an application to prey-predator model with harvesting. Quadratic invariant", Annals of Mathematics and Physics, vol. 7, no. 1, pp. 054–063, 2024. Abstract
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Abdel-Gawad, H. I., "Multiple solitons structures in optical fibers via PNLSE with a novel truncated M-derivative: modulated wave gain", Optical and Quantum Electronics, vol. 56, no. 5: Springer US, pp. 1–21, 2024. Abstract
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Abdel-Gawad, H. I., "Novel optical solitons patterns via Biswas–Arshed equation with gain or loss. Modulated wave gain", International Journal of Modern Physics B: World Scientific Publishing Company, pp. 2550017, 2024. Abstract
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Abdel-Gawad, H. I., and M. Inc, "Rogue waves in a top-pattern and rogue waves with breathers in Ramani equation with $ømega$-time derivative. Stability of the steady state solution", Chaos, Solitons & Fractals, vol. 180: Pergamon, pp. 114554, 2024. Abstract
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2023
Abdel-Gawad, H. I., M. Tantawy, and A. M. Abdelwahab, "Approximate solutions of fractional dynamical systems based on the invariant exponential functions with an application. A novel double-kernel fractional derivative", Alexandria Engineering Journal, vol. 77: Elsevier, pp. 341–350, 2023. Abstract
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Abdel-Gawad, H. I., "Approximate-analytic optical soliton solutions of a modified-Gerdjikov–Ivanov equation: modulation instability", Optical and Quantum Electronics, vol. 55, no. 4: Springer US New York, pp. 298, 2023. Abstract
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Abdel-Gawad, H. I., "Dynamics of steady, unsteady flows and heat transfer in Casson fluid over a free stretching surface: stability analysis", Waves in Random and Complex Media: Taylor & Francis, pp. 1–19, 2023. Abstract
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Abdel-Gawad, H. I., N. H. Sweilam, S. M. AL-Mekhlafi, and D. Baleanu, "Exact solutions of the fractional time-derivative Fokker–Planck equation: A novel approach", Mathematical Methods in the Applied Sciences, vol. 46, no. 7, pp. 7861–7874, 2023. Abstract
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Abdel-Gawad, H. I., "Field and reverse field solitons in wave-operator nonlinear Schrödinger equation with space-time reverse: Modulation instability", Communications in Theoretical Physics, vol. 75, no. 6: IOP Publishing, pp. 065005, 2023. Abstract
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Alqhtani, M., R. Srivastava, H. I. Abdel-Gawad, J. E. Mac{\'ıas-D{\'ıaz, K. M. Saad, and W. M. Hamanah, "Insight into Functional Boiti–Leon–Mana–Pempinelli Equation and Error Control: Approximate Similarity Solutions", Mathematics, vol. 11, no. 22: MDPI, pp. 4569, 2023. Abstract
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Abdel-Gawad, H. I., M. Tantawy, and A. M. Abdelwahab, "A new technique for solving Burgers-Kadomtsev-Petviashvili equation with an external source. Suppression of wave breaking and shock wave", Alexandria Engineering Journal, vol. 69: Elsevier, pp. 167–176, 2023. Abstract
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Abdel-Gawad, H. I., "Rhombus-shaped, M-shaped-solitons, 2D-lumps vector and tunneling in perturbed Gerdjikov–Ivanov equation with fourth-order dispersion: Modulation instability and global bifurcation", Journal of Nonlinear Optical Physics & Materials: World Scientific Publishing Company, pp. 2350077, 2023. Abstract
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Abdel-Gawad, H. I., T. A. Sulaiman, and H. F. Ismael, "Study of a nonlinear Schrodinger equation with truncated M proportional derivative", Optik, vol. 290: Urban & Fischer, pp. 171252, 2023. Abstract
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Abdel-Gawad, H. I., "Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE", Nonlinear Dynamics, vol. 111, no. 2: Springer Netherlands Dordrecht, pp. 1607–1624, 2023. Abstract
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2022
Tantawy, M., and H. I. Abdel-Gawad, "Complex physical phenomena of a generalized (3+ 1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a two-layer heterogeneous liquid", The European Physical Journal Plus, vol. 137, no. 9: Springer Berlin Heidelberg, pp. 1–16, 2022. Abstract
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Abdel-Gawad, H. I., "Continuum soliton chain analog to Heisenberg spin chain system. Modulation stability and spectral characteristics", International Journal of Theoretical Physics, vol. 61, no. 7: Springer US New York, pp. 188, 2022. Abstract
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Abdel-Gawad, H. I., "The eigenvalue problem of the general Einstein–Weyl metric equation and exact self-similar and multi-traveling waves solutions", Indian Journal of Physics: Springer India, pp. 1–7, 2022. Abstract
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Abdel-Gawad, H. I., M. S. Abou-Dina, A. F. Ghaleb, and M. Tantawy, "Heat traveling waves in rigid thermal conductors with phase lag and stability analysis", Acta Mechanica, vol. 233, no. 7: Springer Vienna, pp. 2527–2539, 2022. Abstract
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Abdel-Gawad, H. I., "Inelastic Soliton Interactions for Nonlinear Directional Couplers in Optical Metamaterials with Kerr Nonlinearity Modulation Stability", Journal of Nonlinear Optical Physics & Materials, vol. 31, issue 3, pp. 2250016, 2022.
Abdel-Gawad, H. I., "Inelastic soliton interactions for nonlinear directional couplers in optical metamaterials with Kerr nonlinearity modulation stability", Journal of Nonlinear Optical Physics & Materials, vol. 31, no. 03: World Scientific Publishing Company, pp. 2250016, 2022. Abstract
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Abdel-Gawad, H. I., "Intricate and multiple chirped waves geometric structures solutions of two-mode KdV equation, spectral and stability analysis", International Journal of Modern Physics B, vol. 36, no. 14: World Scientific Publishing Company, pp. 2250056, 2022. Abstract
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Abdel-Gawad, H. I., M. Tantawy, E. S. FAhmy, and C. Park, "Langmuir waves trapping in a (1+ 2) dimensional plasma system. Spectral and modulation stability analysis", Chinese Journal of Physics, vol. 77: Elsevier, pp. 2148–2159, 2022. Abstract
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Abdel-Gawad, H. I., A. A. Aldailami, K. M. Saad, and J. F. Gómez-Aguilar, "Numerical solution of q-dynamic equations", Numerical Methods for Partial Differential Equations, vol. 38, no. 5: John Wiley & Sons, Inc. Hoboken, USA, pp. 1162–1179, 2022. Abstract
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Abdel-Gawad, H. I., and A. H. Abdel-gawad, "On a global continuum model for COVID-19 virus in the presence of vaccine and induced immunity. Stability and initial states control", Alexandria Engineering Journal, vol. 61, no. 11: Elsevier, pp. 9235–9242, 2022. Abstract
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Abdel-Gawad, H. I., "Self-phase modulation via similariton solutions of the perturbed NLSE Modulation instability and induced self-steepening", Communications in Theoretical Physics, vol. 74, no. 8: IOP Publishing, pp. 085005, 2022. Abstract
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Abdel-Gawad, H. I., "Self-steepening, Raman scattering and self-phase modulation-interactions via the perturbed Chen–Lee–Liu equation with an extra dispersion. Modulation insability and spectral analysis", Optical and Quantum Electronics, vol. 54, no. 7: Springer US New York, pp. 426, 2022. Abstract
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Abdel-Gawad, H. I., M. Tantawy, and M. S. M. Rajan, "Similariton regularized waves solutions of the (1+ 2)-dimensional non-autonomous BBME in shallow water and stability", Journal of Ocean Engineering and Science, vol. 7, no. 4: Elsevier, pp. 321–326, 2022. Abstract
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Abdel-Gawad, H. I., M. Tantawy, and A. M. Abdelwahab, "Similarity solutions of a generalized inhomogeneous-nonautonomous (2+ 1)-dimensional Konopelchenko–Dubrovsky equation. Stability analysis", Alexandria Engineering Journal, vol. 61, no. 12: Elsevier, pp. 11225–11237, 2022. Abstract
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Abdel-Gawad, H. I., "Similarity solutions of the steady-state MHD flow with in-homogeneous viscosity over stretching surfaces with free boundary, stability analysis.", Mathematics in Engineering, Science & Aerospace (MESA), vol. 13, no. 2, 2022. Abstract
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Abdel-Gawad, H. I., and M. R. Belic, "Similarity solutions of the surface waves equation in (2+ 1) dimensions and bifurcation", Applied Mathematics and Nonlinear Sciences, 2022. Abstract
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2021
Abdel-Gawad, H. I., M. Tantawy, B. Abd El-Aziz, and A. Bekir, "Analytic Solutions of Fractal and Fractional Time Derivative-Burgers–Nagumo Equation", International Journal of Applied and Computational Mathematics, vol. 7, issue 6, pp. 1-14, 2021.
Abdel-Gawad, H. I., "Chirped, breathers, diamond and W-shaped optical waves propagation in nonself-phase modulation medium. Biswas–Arshed equation", International Journal of Modern Physics B: World Scientific Publishing Company, pp. 2150097, 2021. Abstract
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Abdel-Gawad, H. I., and M. Tantawy, "Coupled self-similar-traveling optical wave tunneling induced by an injected light beam", Waves in Random and Complex Media, vol. 31, issue 6, pp. 1623-1632, 2021.
Abdel-Gawad, H. I., and A. H. Abdel-gawad, "Discrete and continuum models of COVID-19 virus, formal solutions, stability and comparison with real data", Mathematics and Computers in Simulation, vol. 190, pp. 222-230, 2021.
Abdel-Gawad, H. I., "The eigenvalue problem of the general Einstein–Weyl metric equation and exact self-similar and multi-traveling waves solutions", Indian Journal of Physics: Springer India, pp. 1-7, 2021. Abstract
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Abdel‐Gawad, H. I., N. H. Sweilam, S. M. Al‐Mekhlafi, and D. Baleanu, "Exact solutions of the fractional time‐derivative Fokker–Planck equation: A novel approach", Mathematical Methods in the Applied Sciences, 2021. Abstract
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Abdel-Gawad, H. I., "A generalized Kundu--Eckhaus equation with an extra-dispersion: pulses configuration", Optical and Quantum Electronics, vol. 53, issue 12, pp. 1-16, 2021.
Abdel-Gawad, H. I., "Infinite solitons in ferromagnetic materials with an internal magnetic field", Modern Physics Letters B, vol. 35, issue 25, pp. 2150413, 2021.
Abdel-Gawad, H. I., and C. Park, "Interactions of pulses Produced by Two-mode Resonant Nonlinear Schrodinger Equations", Results in Physics: Elsevier, pp. 104113, 2021. Abstract
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Abdel-Gawad, H. I., H. M. Abdel-Rashid, M. Tantawy, and G. H. Ibrahim, "Multi-geometric structures of thermophoretic waves transmission in (2+ 1) dimensional graphene sheets. Stability analysis", International Communications in Heat and Mass Transfer, vol. 126, pp. 105406, 2021.
Alderremy, A. A., H. I. Abdel-Gawad, K. M. Saad, and S. Aly, "New exact solutions of time conformable fractional Klein Kramer equation", Optical and Quantum Electronics, vol. 53, issue 12, pp. 1-14, 2021.
Abdel-Gawad, H. I., and M. Tantawy, "A novel model for lasing cavities in the presence of population inversion: Bifurcation and stability analysis", Chaos, Solitons & Fractals, vol. 144: Pergamon, pp. 110693, 2021. Abstract
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Tantawy, M., and H. I. Abdel-Gawad, "On continuum model analog to zig-zag optical lattice in quantum optics", Applied Physics B, vol. 127, issue 8, pp. 1-9, 2021.
Abdel-Gawad, H. I., M. Tantawy, T. N. Nkomom, and J. B. Okaly, "On the dynamics of DNA molecules with an-harmonics potential in the normal and damaged states", Physica Scripta, vol. 96, issue 12, pp. 125246, 2021.
Abdel-Gawad, H. I., M. Tantawy, and M. S. M. Rajan, "Similariton regularized waves solutions of the (1+ 2)-dimensional non-autonomous BBME in shallow water and stability", Journal of Ocean Engineering and Science, 2021.
Abdel-Gawad, H. I., "Solutions of the generalized transient stimulated Raman scattering equation. Optical pulses compression", Optik, vol. 230: Urban & Fischer, pp. 166314, 2021. Abstract
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Abdel-Gawad, H. I., "Study of modulation instability and geometric structures of multisolitons in a medium with high dispersivity and nonlinearity", Pramana, vol. 95, issue 3, pp. 1-9, 2021.
Abdel-Gawad, H. I., D. Baleanu, and A. H. Abdel-gawad, "Unification of the different fractional time derivatives: An application to the epidemic-antivirus dynamical system in computer networks", Chaos, Solitons & Fractals, vol. 142: Pergamon, pp. 110416, 2021. Abstract
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Abdel-Gawad, H. I., "Zig-zag, bright, short and long solitons formation in inhomogeneous ferromagnetic materials. Kraenkel-Manna-Merle equation with space dependent coefficients", Physica Scripta, vol. 96, issue 12, pp. 125212, 2021.
2020
Abdel-Gawad, H. I., M. Tantawy, and J. A. Tenreiro Machado, "Abundant structures of waves in plasma transitional layer sheath", Chinese Journal of Physics, vol. 67: Elsevier, pp. 147-154, 2020. Abstract
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Abdel-Gawad, H., "An Approach to Solutions of Fractal and Fractional Time Derivative Fokker-Planck Equation", Authorea Preprints: Authorea, 2020. Abstract
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Abdel-Gawad, H. I., M. Tantawy, M. Inc, and A. Yusuf, "Construction of rogue waves and conservation laws of the complex coupled Kadomtsev–Petviashvili equation", International Journal of Modern Physics B, vol. 34, issue 12: World Scientific Publishing Company, pp. 2050115, 2020. Abstract
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Abdel-Gawad, H. I., N. H. Sweilam, S. M. Al-Mekhlafi, and D. Baleanu, "Exact Solutions of the Time Derivative Fokker-Planck Equation: A Novel Approach", arXiv preprint arXiv:2008.02801, 2020. Abstract
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Abdel‐Gawad, H. I., M. Tantawy, and D. Baleanu, "Fractional KdV and Boussenisq‐Burger's equations, reduction to PDE and stability approaches", Mathematical Methods in the Applied Sciences, vol. 43, issue 7, pp. 4125-4135, 2020. Abstract
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Tantawy, M., H. I. Abdel-Gawad, and A. F. Ghaleb, "New results for the effects of higher-order moduli and material properties on strain waves propagating through elastic circular cylindrical rods", The European Physical Journal Plus, vol. 135, issue 1: Springer Berlin Heidelberg, pp. 1-12, 2020. Abstract
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Tantawy, M., and H. I. Abdel-Gawad, "On multi-geometric structures optical waves propagation in self-phase modulation medium: Sasa–Satsuma equation", The European Physical Journal Plus, vol. 135, issue 11: Springer Berlin Heidelberg, pp. 1-10, 2020. Abstract
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Tantawy, M., and H. I. Abdel-Gawad, "On the dynamics of inhomogeneous short-range DNA interactions at a defect", The European Physical Journal Plus, vol. 135, issue 5: Springer Berlin Heidelberg, pp. 396, 2020. Abstract
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Srivastava, H. M., H. I. Abdel-Gawad, and K. M. Saad, "Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions", Discrete & Continuous Dynamical Systems-S: American Institute of Mathematical Sciences, 2020. Abstract
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Srivastava, H. M., H. I. Abdel-Gawad, and K. M. Saad, "Stability of traveling waves based upon the Evans function and Legendre polynomials", Applied Sciences, vol. 10, issue 3: Multidisciplinary Digital Publishing Institute, pp. 846, 2020. Abstract
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2019
Abdel-Gawad, H. I., and M. Tantawy, "Coupled self-similar-traveling optical wave tunneling induced by an injected light beam", Waves in Random and Complex Media, 2019.
application/pdf iconcoupled_self_similar_traveling_optical_wave_tunneling_induced_by_an_injected_light_beam.pdf
Inc, M., H. I. Abdel-Gawad, and M.Tantawy, "On multiple soliton similariton-pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media", Mah. Meth. in the Appl. Sci, issue On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Ka, 2019. hamdy-2019-mathematical_methods_s_1.pdf
Abdel-Gawad, H. I., A. Q. Biswad, A. R. Elshomrani, and M.Belic, "Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials", Results in Physics, vol. 15, pp. 102707, 2019.
application/pdf iconoptical_solitons.pdf
Abdel-Gawad, H. I., and M. Tantawy, "Two-layer fluid formation and propagation of periodic solitons induced by (3+ 1)-dimensional KP equation", Computer and Mathematics with Applications, vol. 78, pp. 2011-2017, 2019.
application/pdf iconabdel-gawad2019.pdf
2018
Abdel-Gawad, H. I., M. Tantawy, M. Inc, and A. Yusuf, "On multi-fusion solitons induced by inelastic collision for quasi-periodic propagation with nonlinear refractive index and stability analysis", Modern Physics Letters B, vol. 32, issue 29, 2018.
Abdel-Gawad, H. I., and M. Tantawy, "Rogue Waves in Multiple-Solitons–Inelastic Collisions—The complex Sharma–Tasso–Olver Equation", Modern Physics Letters B, vol. 32, issue 8, 2018.
Osman, M. S., H. I. Abdel-Gawad, and E. M. A. Mahdy, "Two-Layer-Atmospheric Blocking in a Medium with High Nonlinearity and Lateral Dispersion", Results in Physics, vol. 8, pp. 1054-1060, 2018.
application/pdf icontwolayeratmospheric.pdf
2017
Abdel-Gawad, H. I., A. M. El-Shrae, and K. M. Saad, "Criterion of Existence of Realistic Permanent Travelling Wave Solutions in Reaction Diffusion Systems", Communications in Numerical Analysis, vol. 1, pp. 50-79, 2017.
application/pdf iconarticle_5.pdf
Abdel-Gawad, H. I., and M. Tantawy, "Mixed-type soliton propagations in two-layer-liquid (or in an elastic) medium with dispersive waveguides", Journal of Molecular Liquids, vol. 241, pp. 870-874, 2017.
Abdel-Gawad, H. I., and M. Tantawy, "On controlled propagation of long waves in nonautonomous Boussinesq–Burgers equations", Nonlinear Dyn, vol. 87, pp. 2511–2518, 2017.
Abdel-Gawad, H. I., and M. Tantawy, "On multi-graded-index soliton solutions for the Boussinesq-Burgers equations in optical communications", Optics Communications, vol. 384, pp. 7-10, 2017.
Abdel-Gawad, H. I., and M. Tantawy, "On N-mixed-type soliton propagation in dispersive nonautonomous long waves with waveguides", Nonlinear Dyn, vol. 90, pp. 233-239, 2017.
Abdel-Gawad, H. I., and M. Tantawy, "On The Features Solitary Wave Solutions for the Double-Structures Model of DNA", International Journal of Research Studies in Biosciences (IJRSB), vol. 5, issue 3, pp. 34-40, 2017.
Abdel-Gawad, H. I., and M. Tantawy, "Propagation of high and low graded-index waveguides in an inhomogeneous-dispersive medium", Superlattices and Microstructures, vol. 111, pp. 991-999, 2017.
Abdel-Gawad, H. I., and M. Tantawy, "Waveguides of two-soliton solutions for the coupled KdV equations with variable coefficients in long-distance communication systems", Indian J Phys, vol. 91, issue 6, pp. 671–675, 2017.
2016
, "Dynamic of DNA’s possible impact on its damage", Math. Meth. Appl. Sci., vol. 39, pp. 168–176, 2016. dynamic_of_dnas_possible_impact_on_its_damage.pdf
, "MULTI-SOLITON SOLUTIONS BASED ON INTERACTIONS OF BASIC TRAVELING WAVES WITH AN APPLICATION TO THE NONLOCAL BOUSSINESQ EQUATION", ACTA PHYSICA POLONICA B, vol. 47, issue 4, pp. 1101-1112, 2016. multi-soliton_solutions_based_on.pdf
, "On the extension of solutions of the real to complex KdV equation and a mechanism for the construction of rogue waves", Waves in Random and Complex Media, vol. 26, issue 3, pp. 397–406, 2016. solutions_of_the_real_to_complex_kdv_equation_and_construction_of_rogue_waves.pdf
, "On the “kˆp-operator”, new extension of the KdV6 to (m+1)-dimensional equation and traveling waves solutions", Nonlinear Dynamics, vol. 85, issue 3, pp. 1509–1515, 2016. on_the_kp-operator_new_extension_of_the_kdv6.pdf
2015
and Abdel-Gawad, H. I., T. M., , Discrete and continuum modeling of DNA dynamics and stability analysis,, , , Berlin,, Lambert academic publishing,, 2015.
Abdel-Gawad, H. I., and M. S. Osman, "On shallow water waves in a medium with 5 time-dependent dispersion and nonlinearity 6 coefficients", Journal of advanced Research, vol. To appear, 2015.
2014
Abdel-Gawad, H. I., and M. Tantawy, Discrete and continuum modeling of DNA dynamics and stability analysis, , Berlin, Lambert academic publishing, 2014.
Osman, M. S., and H.I.Abdel-Gawad, Exact solutions of evolution equations with variable coefficients, , Berlin, Lambert academic publishing, 2014.
Abdel-Gawad, H. I., and M. S. Osman, "Exact solutions of the Korteweg-de Vries equation with space and time dependent coefficients by the extended unified method Authors Hamdy I. Abdel-Gawad, Mohamed Osman Publication date 2014/2 Journal Indian Journal of Pure and Applied Mathematics Volume 4", Indian j. pure nd Appl. Math., vol. 45, pp. 1-12, 2014.
Abdel-Gawad, H. I., and M. Tantawy, "Exact Solutions of the Schamel-Korteweg equation With time dependent Coefficients", Info. Sci.Lett., vol. 3, pp. 103-109, 2014.
Abdel-Gawad, H. I., "Waves in deep water based on the nonlinear Schrödinger equation with variable coefficients", Canadian Journal of Physics, vol. 92, pp. 1158-1165, 2014. cjp-2013-0327.pdf
2013
Abdel-Gawad, H. I., N. S. Elazab, and M. OSMAN, "Exact Solutions of Space Dependent Korteweg–de Vries Equation by The Extended Unified Method", Journal of the Physical Society of Japan, vol. 82, pp. 044004-1-044004-4, 2013. Abstractjpsj-82-044004_1.pdf

Recently the unified method for finding traveling wave solutions of nonlinear evolution equations was proposed by one of the authors (HIAG). It was shown that, this method unifies all the methods being used to find these solutions. In this paper, we extend this method to find a class of formal exact solutions to Korteweg–de Vries equation with space dependent coefficients.

Abdel-Gawad, H. I., and M. S. Osman, "On the Variational Approach for Analyzing the Stability of Solutions of Evolution Equations", KYUNGPOOK Math. J., vol. 83, pp. 661-680, 2013. Abstractkmj-53-4-661.pdf

KYUNGPOOK Math. J.The eigenvalue problems arise in the analysis of stability of traveling waves or rest state solutions are currently dealt with, using the Evans function method. In the literature, it had been shown that, use of this method is not straightforward even in very simple examples. Here an extended \variational" method to solve the eigenvalue problem for the higher order di erential equations is suggested. The extended method is matched to the well known variational iteration method. The criteria for validity of the eigenfunctions and eigenvalues obtained is presented. Attention is focused to nd eigenvalue and eigenfunction solutions of the Kuramoto-Slivashinsky and (K[p,q]) equation.

2012
Abdel-Gawad, H. I., "Towards a Unified Method for Exact Solutions of Evolution Equations. An Application to Reaction Diffusion Equations with Finite Memory Transport", Journal of Statistical Physics, vol. 147, no. 3: Springer, pp. 506–518, 2012. Abstract
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2010
Abdel-Gawad, H. I., and A. A. Aldailami, "On< i> q-dynamic equations modelling and complexity", Applied Mathematical Modelling, vol. 34, no. 3: Elsevier, pp. 697–709, 2010. Abstract
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Abdel-Gawad, H. I., and A. A. Aldailami, "On< i> q-dynamic equations modelling and complexity", Applied Mathematical Modelling, vol. 34, no. 3: Elsevier, pp. 697–709, 2010. Abstract
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2008
Abdel-Gawad, H. I., "A model for a finite memory transport in the Fisher equation", Applied Mathematical Modelling, vol. 32, no. 9: Elsevier, pp. 1883–1893, 2008. Abstract
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Abdel-Gawad, H. I., "A model for a finite memory transport in the Fisher equation", Applied Mathematical Modelling, vol. 32, no. 9: Elsevier, pp. 1883–1893, 2008. Abstract
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2003
Abdel-Gawad, H. I., "A method for finding the invariants and exact solutions of coupled non-linear differential equations with applications to dynamical systems", International journal of non-linear mechanics, vol. 38, no. 4: Elsevier, pp. 429–440, 2003. Abstract
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2001
Abdel-Gawad, H. I., and H. A. Abdusalam, "Approximate solutions of the Kuramoto–Sivashinsky equation for periodic boundary value problems and chaos", Chaos, Solitons & Fractals, vol. 12, no. 11: Elsevier, pp. 2039–2050, 2001. Abstract
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Abdel-Gawad, H. I., and H. A. Abdusalam, "Approximate solutions of the Kuramoto–Sivashinsky equation for periodic boundary value problems and chaos", Chaos, Solitons & Fractals, vol. 12, no. 11: Elsevier, pp. 2039–2050, 2001. Abstract
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2000
Abdel-Gawad, H. I., and A. M. El-Shrae, "An approach to solutions of coupled semilinear partial differential equations with applications", Mathematical methods in the applied sciences, vol. 23, no. 10: Wiley Online Library, pp. 845–864, 2000. Abstract
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Abdel-Gawad, H. I., and A. M. El-Shrae, "An approach to solutions of coupled semilinear partial differential equations with applications", Mathematical methods in the applied sciences, vol. 23, no. 10: Wiley Online Library, pp. 845–864, 2000. Abstract
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1999
Abdel-Gawad, H. I., "On the behavior of solutions of a class of nonlinear partial differential equations", Journal of statistical physics, vol. 97, no. 1-2: Springer, pp. 395–407, 1999. Abstract
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Abdel-Gawad, H. I., "On the behavior of solutions of a class of nonlinear partial differential equations", Journal of statistical physics, vol. 97, no. 1-2: Springer, pp. 395–407, 1999. Abstract
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1991
Abdel-Gawad, H. I., "Solutions of the equation. Exact solutions of some partial differential equations in mechanics and physics", Mathematical methods in the applied sciences, vol. 14, pp. 615–631, 1991. Abstract
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1990
Abdel-Gawad, H. I., "Solution of a class of partial differential equations. Some diffusion equations", Mathematical methods in the applied sciences, vol. 12, no. 3: Wiley Online Library, pp. 221–228, 1990. Abstract
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Tourism