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and Abdel-Gawad, H. I., T. M., , Discrete and continuum modeling of DNA dynamics and stability analysis,, , , Berlin,, Lambert academic publishing,, 2015.
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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. 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., 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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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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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., 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., 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., 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.
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Abdel-Gawad, H. I., and M. Tantawy, Discrete and continuum modeling of DNA dynamics and stability analysis, , Berlin, Lambert academic publishing, 2014.
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.
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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., 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., 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., 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., 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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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.
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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., "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., 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, 2022.
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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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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., "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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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.
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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.
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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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., 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., 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.
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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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.
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., 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. 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.
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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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.
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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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. 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.

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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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.
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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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.
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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.
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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, 2021.
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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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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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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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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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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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.
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.
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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., 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.
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
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Tourism