THERMAL SCIENCE

International Scientific Journal

Raghda A. M. Attia

,

Sayed K. Elagan

,

Meteub R. Alharthi

,

Mostafa M. A. Khater

NEW TYPES OF EXACT SOLUTIONS OF HIGH-FREQUENCY WAVES MODEL IN THE RELAXATION MEDIUM

ABSTRACT
In this article, based on the extended fan-expansion method, novel soliton wave solutions of the Vakhnenko-Parkes equation are constructed. The stable property of the obtained analytical solutions is tested by implementing the Hamiltonian system's characterizations. The applied method is effective and applicable for many problems of non-linear PDE in mathematical physics.
KEYWORDS
Vakhnenko-Parkes equation, extended fan-expansion method, stable property, soliton wave solutions
PAPER SUBMITTED: 2021-03-12
PAPER REVISED: 2021-03-27
PAPER ACCEPTED: 2021-04-08
PUBLISHED ONLINE: 2021-12-18
DOI REFERENCE: https://doi.org/10.2298/TSCI21S2233A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Special issue 2, PAGES [233 - 238]
REFERENCES
  1. Khater, M. M. A., et al., Analytical and Semi-Analytical Solutions for Phi-Four Equation Through Three Recent Schemes, Results in Physics, 22 (2021), Mar., 103954
  2. , M. M. A., et al., Numerical Investigation for the Fractional Non-linear Space‐Time Telegraph Equation Via the Trigonometric Quintic B‐Spline Scheme, Mathematical Methods in the Applied Sciences, 44 (2021), 6, pp. 4598-4606
  3. Khater, M.M. A., et al., Diverse Accurate Computational Solutions of the Non-linear Klein-Fock-Gordon equation, Results in Physics, 23 (2021), Apr., 104003
  4. Khater, M. M. A., Behzad, G., On the Solitary Wave Solutions and Physical Characterization of Gas Diffusion in a Homogeneous Medium Via Some Efficient Techniques, The European Physical Journal Plus, 136 (2021), 4, pp. 1-28
  5. Khater, M. M. A., et al., Novel Computational and Accurate Numerical Solutions of the Modified Benjamin-Bona-Mahony (BBM) Equation Arising in the Optical Illusions Field, Alexandria Engineering Journal, 60 (2021), 1, pp. 1797-1806
  6. Attia, R. A. M., et al., Computational and Numerical Simulations for the Deoxyribonucleic Acid (DNA) Model, Discrete & Continuous Dynamical Systems-S, 14 (2021), 10, pp. 3459-3478
  7. Khater, M. M. A., et al., Optical Soliton Structure of the Sub-10-Fs-Pulse Propagation Model, Journal of Optics, 50 (2021), 1, pp. 109-119
  8. Abdel-Aty, A.-H., et al., Oblique Explicit Wave Solutions of the Fractional Biological Population (BP) and Equal Width (EW) Models, Advances in Difference Equations, 20.1 (2020), 1, pp. 1-17
  9. Khater, M. M. A., et al., Two Effective Computational Schemes for a Prototype of an Excitable System, AIP Advances, 10 (2020), 10, 105120
  10. Khater, M. M. A., et al., On Semi Analytical and Numerical Simulations for a Mathematical Biological Model; the Time-Fractional Non-linear Kolmogorov-Petrovskii-Piskunov (KPP) Equation, Chaos, Solitons & Fractals, 144 (2021), Mar., 110676
  11. Khater, M. M. A., et al., Abundant New Solutions of the Transmission of Nerve Impulses of an Excitable System, The European Physical Journal Plus, 135 (2020), 2, pp. 1-12
  12. Yue, C., et al., Computational Simulations of the Couple Boiti-Leon-Pempinelli (BLP) System and the (3+1)-Dimensional Kadomtsev-Petviashvili (KP) Equation, AIP Advances, 10 (2020), 4, 045216
  13. Chu, Y., et al., Diverse Novel Analytical and Semi-Analytical Wave Solutions of the Generalized (2+1)-Dimensional Shallow Water Waves Model, AIP Advances, 11 (2021), 1, 015223
  14. Yue, C., et al., Abundant Analytical Solutions of the Fractional Non-linear (2+1)-Dimensional BLMP Equation Arising in Incompressible Fluid, International Journal of Modern Physics B, 34 (2020), 9, 2050084
  15. Khater, M. M. A., et al., Abundant Stable Computational Solutions of Atangana-Baleanu Fractional Non-linear HIV-1 Infection of CD4+ T-Cells of Immunodeficiency Syndrome, Results in Physics, 22 (2021), Mar., 103890
  16. Yue, C., et al., On Explicit Wave Solutions of the Fractional Non-linear DSW System Via the Modified Khater Method, Fractals, 28 (2020), 8, 2040034
  17. Khater, M.M. A., et al., Effective Computational Schemes for a Mathematical Model of Relativistic Elec-trons Arising in the Laser Thermonuclear Fusion, Results in Physics, 19 (2020), Dec., 103701
  18. Khater, M.M. A., et al., Computational Analysis of a Non-linear Fractional Emerging Telecommunication Model with Higher-Order Dispersive Cubic-Quintic, Information Sciences Letters, 9 (2020), 2, 4
  19. Vakhnenko, V. O., Parkes, E. J. Approach in Theory of Non-linear Evolution Equations: The Vakhnenko-Parkes Equation, Advances in Mathematical Physics, 2016 (2016), ID 2916582
  20. Roshid, H.-O., et al., Investigation of Solitary wave Solutions for Vakhnenko-Parkes Equation Via Exp-function and Exp (− ϕ (ξ))-Expansion Method, SpringerPlus, 3 (2014), 1, pp. 1-10
  21. Khan, K., Akbar, M. A., The exp (− ϕ (ξ))-Expansion Method for Finding Travelling Wave Solutions of Vakhnenko-Parkes Equation, International Journal of Dynamical Systems and Differential Equations, 5 (2014), 1, pp. 72-83
  22. Vakhnenko, V. O., Parkes, E. J., Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation, Progress of Theoretical Physics, 127 (2012), 4, pp. 593-613
  23. Vakhnenko, V. O., Parkes, E. J., The Two Loop Soliton Solution of the Vakhnenko Equation, Non-line-arity, 11 (1998), 6, 1457
  24. Majid, F., et al., Solitary Wave Solutions of the Vakhnenko-Parkes Equation, Non-linear Analysis: Mod-elling and Control, 17 (2012), 1, pp. 60-66
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New types of exact solutions of high-frequency waves model in the relaxation medium

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence