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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, general theory
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[1] DOI: 10.1103/PhysRevLett.58.2615 · doi:10.1103/PhysRevLett.58.2615
[2] DOI: 10.1103/PhysRevD.37.1472 · doi:10.1103/PhysRevD.37.1472
[3] DOI: 10.1103/PhysRevD.38.1310 · doi:10.1103/PhysRevD.38.1310
[4] DOI: 10.1103/PhysRevD.38.1310 · doi:10.1103/PhysRevD.38.1310
[5] DOI: 10.1103/PhysRevD.38.2518 · doi:10.1103/PhysRevD.38.2518
[6] DOI: 10.1103/PhysRevD.38.2526 · doi:10.1103/PhysRevD.38.2526
[7] DOI: 10.1063/1.528057 · Zbl 0783.58087 · doi:10.1063/1.528057
[8] DOI: 10.1103/PhysRevD.38.723 · doi:10.1103/PhysRevD.38.723
[9] DOI: 10.1103/PhysRev.85.631 · Zbl 0046.21501 · doi:10.1103/PhysRev.85.631
[10] DOI: 10.1007/BF01646496 · Zbl 0127.19706 · doi:10.1007/BF01646496
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