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Deciphering nonlinear wave phenomena in Einstein’s vacuum field equation using analytical and numerical approaches

Author

Listed:
  • Amer, Aamna
  • Jaradat, Emad K.
  • Ur Rehman, Hamood
  • Abo-Dahab, S.M.
  • Hafez, Ramy M.
  • Yildirim, Yakup

Abstract

The current paper explores the Einstein’s vacuum field equation utilizing both analytical and numerical approaches. This model emerges in mathematical physics, has significant applications in the theory of general relativity. Numerous ambitious experiments and space missions are momentously influenced by the governing model. For the analytical analysis, we employ the modified extended tanh method with the Riccati equation and the new Kudryashov’s method, that results in multiple compelling soliton solutions. We employ the differential transform method as a numerical tool to validate and confirm the accuracy of the derived analytical solutions. Furthermore, we provide certain assessment tables and graphical depictions to supplement the findings of the study. The in-depth exploration of soliton solutions not only enhances our understanding of basic wave phenomena but also provides valuable perspectives for addressing nonlinear equations in various scientific areas.

Suggested Citation

  • Amer, Aamna & Jaradat, Emad K. & Ur Rehman, Hamood & Abo-Dahab, S.M. & Hafez, Ramy M. & Yildirim, Yakup, 2026. "Deciphering nonlinear wave phenomena in Einstein’s vacuum field equation using analytical and numerical approaches," Chaos, Solitons & Fractals, Elsevier, vol. 208(P4).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p4:s0960077926005126
    DOI: 10.1016/j.chaos.2026.118371
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