Asymptotic Analysis of Nonlinear Emden-Fowler Equations Using the WKB Method
Keywords:
Emden-Fowler equations, WKB approximation method, asymptotic analysis, nonlinear differential equations, Hardy formulation, compact solutions, blow-up phenomena, singular perturbation theoryAbstract
This research paper investigates the asymptotic properties of solutions to nonlinear Emden-Fowler equations through the application of the WKB (Wentzel-Kramers-Brillouin) method. We systematically analyze three distinct categories of solutions: globally extendable solutions, non-extendable solutions, and compactly supported (finite) solutions. The construction of the Hardy-form WKB solution is rigorously derived, and its asymptotic validity is formally proven. The theoretical results obtained in this study provide valuable insights for numerical modeling of nonlinear phenomena across various physical domains, offering enhanced accuracy in asymptotic approximations.
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