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Analytical and numerical solutions to the nonlinear Klein-Gordon equation using improved Kudryashov and modified rational methods Cover

Analytical and numerical solutions to the nonlinear Klein-Gordon equation using improved Kudryashov and modified rational methods

Open Access
|Dec 2025

References

  1. LeFloch P.G., Mena F.C., Nguyen T.C., Spherically symmetric evolution of self-gravitating massive fields, Journal of Differential Equations, 394, 31–97, 2024.
  2. Wang R., Shi D., Superconvergence analysis of an H1-Galerkin mixed FEM for Klein-Gordon-Zakharov equations with power law nonlinearity, Communications in Nonlinear Science and Numerical Simulations, 130, 107787, 2024.
  3. Tanriverdi T., Baskonus H.M., Mahmud A.A., Muhamad K.A., Explicit solution of fractional order atmosphere-soil-land plant carbon cycle system, Ecological Complexity, 48, 100966, 2021.
  4. Mahmud K.A., Tanriverdi T., Mahmud A.A., Baskonus H.M., Interaction characteristics of the Riemann wave propagation in the (2+1)-dimensional generalized breaking soliton system, International Journal of Computer Mathematics, 100(6), 1340–1355, 2023.
  5. Mahmud A.A., Tanriverdi T., Mahmud K.A., Exact traveling wave solutions for (2+1)-dimensional Konopelchenko-Dubrovsky equation by using the hyperbolic trigonometric functions methods, International Journal of Mathematics and Computer in Engineering, 1(1), 11–24, 2023.
  6. Baskonus H.M., Mahmud A.A., Mahmud K.A., Tanriverdi T., A study on Caudrey–Dodd–Gibbon–Sawada–Kotera partial differential equation, Mathematical Methods in the Applied Sciences, 45(14), 8737–8753, 2022.
  7. Mahmud A.A., Baskonus H.M., Tanriverdi T., Mahmud K.A., Optical solitary waves and soliton solutions of the (3+1)-dimensional generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation, Computational Mathematics and Mathematical Physics, 63(6), 1085–1102, 2023.
  8. Mahmud A.A., Tanriverdi T., Mahmud K.A., Baskonus H.M., Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation, Journal of Applied Mathematics and Computational Mechanics, 22(2), 36–48, 2023.
  9. Mahmud A.A., Mahmud K.A., Tanriverdi T., Baskonus H.M., An investigation of Fokas system using two new modifications for the trigonometric and hyperbolic trigonometric function methods, Optical and Quantum Electronics, 56, 717, 2024.
  10. Kumari S., Pandey R.K., Alternating direction implicit approach for the two-dimensional time fractional nonlinear Klein-Gordon and Sine-Gordon problems, Communications in Nonlinear Science and Numerical Simulations, 130, 107769, 2024.
  11. Gordillo-Núñez G., Alvarez-Nodarse R., Quintero N.R., The complete solution of the Schrödinger equation with the Rosen-Morse type potential via the Nikiforov-Uvarov method, Physica D Nonlinear Phenomena, 458, 134008, 2024.
  12. Giacomelli G., Politi A., Ultraslow dynamics of free-running ring lasers: Toward a minimal model, Physical Review A, 109(2), 023505, 2024.
  13. Iqbal M., Lu D., Seadawy A.R., Mustafa G., Zhang Z., Ashraf M., Ghaffar A., Dynamical analysis of soliton structures for the nonlinear third-order Klein-Fock-Gordon equation under explicit approach, Optical and Quantum Electronics, 56(4), 651, 2024.
  14. Păuna A.M., The auxiliary equation approach for solving reaction-diffusion equations, Journal of Physics Conference Series, 2719, 012002, 2024.
  15. Lin Q., Pang Y., Wang X., Xu Z., Global well-posedness of solutions for 2-D Klein–Gordon equations with exponential nonlinearity, Journal of Mathematical Physics, 65(2), 021501, 2024.
  16. Amado J.B., Gwak B., Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes, Journal of High Energy Physics, 2024(2), 189, 2024.
  17. Dautov R.Z., Salimzyanova G.R., A conservative fully discrete finite element scheme for the nonlinear Klein–Gordon equation, Uchenye Zapiski Kazanskogo Universiteta Seriya Fiziko-Matematicheskie Nauki, 165(3), 190–207, 2023.
  18. Hou F., Tao F., Yin H., The partial null conditions and global smooth solutions of the nonlinear wave equations on Rd × T with d = 2, 3, Journal of Differential Equations, 378, 823–870, 2024.
  19. Sadoun M.A., Adnane H., Relativistic bound states solutions with a linear combination of Yukawa and deformed Hulthén potentials by path integral approach, International Journal of Geometric Methods in Modern Physics, 21(01), 2450025, 2024.
  20. Heß M., Schneider G., A robust way to justify the derivative NLS approximation, Zeitschrift für Angewandte Mathematik und Physik, 74(6), 224, 2023.
  21. Dudnikova T.V., Transport equation for the harmonic crystal coupled to a Klein–Gordon field, Russian Journal of Mathematical Physics, 30(4), 501–521, 2023.
  22. Guajardo L., Black string spectrum of shift-symmetric Horndeski theories, Physical Review D, 108(12), 124041, 2023.
  23. Van Den Berg J.B., Hénot O., Lessard J.P., Constructive proofs for localised radial solutions of semilinear elliptic systems on Rd, Nonlinearity, 36(12), 6476–6512, 2023.
  24. Izgi Z.P., Analytical simulations of the Q-ball dynamics model in theoretical physics, Modern Physics Letters B, 37(34), 2350165, 2023.
  25. Allakhverdian V., Naumov D.V., Exact analytical solution of the one-dimensional time-dependent radiative transfer equation with linear scattering, Journal of Quantitative Spectroscopy and Radiative Transfer, 310, 108726, 2023.
  26. Qian Y., Zhang Y., Huang Y., Dong S., Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: Error analysis and algorithms, Journal of Computational Physics, 495, 112527, 2023.
  27. Guvendi A., Ahmed F., Relativistic quantum oscillator under rainbow gravity’s effects in traversable wormhole with disclination, International Journal of Modern Physics A, 38(35n36), 2350179, 2023.
  28. Rosenau P., Krylov S., Solitary waves in electro-mechanical lattices, Chaos, 33(12), 123124, 2023.
  29. Podder A., Arefin M.A., Akbar M.A., Uddin M.H., A study of the wave dynamics of the space-time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach, Scientific Reports, 13, 20478, 2023.
  30. Martin-Vergara F., Cuevas-Maraver J., Farrell P.E., Villatoro F.R., Kevrekidis P.G., Discrete breathers in Klein-Gordon lattices: A deflation-based approach, Chaos, 33(11), 113126, 2023.
  31. Javed F., Computational analysis of thin-shell with scalar field for class of new black hole solutions in metric-affine gravity, Annals of Physics, 458(2), 169464, 2023.
  32. Kolkovska N., Dimova M., Kutev N., Finite time blow up of solutions to Klein-Gordon equation with variable coefficients nonlinearities, AIP Conference Proceeding, 2953, 070004, 2023.
Language: English
Submitted on: Mar 21, 2024
Accepted on: Jul 16, 2024
Published on: Dec 14, 2025
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2025 Mostafa M.A. Khater, Aleksander Vokhmintsev, Raghda A.M. Attia, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

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