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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.

##### MSC:
 34A34 Nonlinear ordinary differential equations and systems
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##### 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
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