Analytical and Numerical Approaches to Nonlinear Equations in Holographic Black Hole Backgrounds

Document Type : Research Article

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Canadian Quantum Research Center, 204-3002 32 Ave, Vernon, Canada

Abstract

We investigate nonlinear differential equations arising in holographic models of black hole spacetimes within the AdS/CFT correspondence. Emphasis is placed on analytical approximations and numerical solutions of scalar perturbations and nonlinear wave equations in asymptotically anti-de Sitter black holes. We show how effective potentials lead to boundary value problems governed by nonlinear ordinary differential equations. Analytical methods, such as matched asymptotic expansions and perturbative ans"{a}tze, are compared with spectral numerical approaches. Applications to holographic thermalization, quasinormal spectra, and cosmological analogues are discussed. Our results highlight the interplay between nonlinear analysis and physical interpretation in string-inspired models of gravity.

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 9, Issue 2
September 2025
Pages 287-294

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History

  • Receive Date: 17 September 2025
  • Revise Date: 15 October 2025
  • Accept Date: 08 November 2025
  • Publish Date: 12 November 2025

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