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

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.

کلیدواژه ها:

Nonlinear Wave Equations ، AdS/CFT ، Holography ، black hole