A new perturbative approach to nonlinear problems. (English) Zbl 0684.34008

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.


34A34 Nonlinear ordinary differential equations and systems
Full Text: DOI


[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.