Bender, C. M.; Milton, Kimball A.; Pinsky, Stephen S.; Simmons, L. M. jun. A new perturbative approach to nonlinear problems. (English) Zbl 0684.34008 J. Math. Phys. 30, No. 7, 1447-1455 (1989). Summary: A recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the Lagrangian such as \(\phi^ 4\) by \((\phi^ 2)^{1+\delta}\) and then treating \(\delta\) as a small parameter. It is shown here that the same approach gives excellent results when applied to difficult nonlinear differential equations such as the Lane-Emden, Thomas-Fermi, Blasius and Duffing equations. Cited in 4 ReviewsCited in 102 Documents MSC: 34A34 Nonlinear ordinary differential equations and systems Keywords:quantum field theory; Lane-Emden; Thomas-Fermi; Blasius; Duffing equations PDF BibTeX XML Cite \textit{C. M. Bender} et al., J. Math. Phys. 30, No. 7, 1447--1455 (1989; Zbl 0684.34008) Full Text: DOI References: [1] DOI: 10.1103/PhysRevLett.58.2615 [2] DOI: 10.1103/PhysRevD.37.1472 [3] DOI: 10.1103/PhysRevD.38.1310 [4] DOI: 10.1103/PhysRevD.38.1310 [5] DOI: 10.1103/PhysRevD.38.2518 [6] DOI: 10.1103/PhysRevD.38.2526 [7] DOI: 10.1063/1.528057 · Zbl 0783.58087 [8] DOI: 10.1103/PhysRevD.38.723 [9] DOI: 10.1103/PhysRev.85.631 · Zbl 0046.21501 [10] DOI: 10.1007/BF01646496 · Zbl 0127.19706 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.