Solutions of a nonlinear partial differential equation of hyperbolic type
Author:
C. E. Billigheimer
Journal:
Quart. Appl. Math. 25 (1967), 19-30
MSC:
Primary 35.36
DOI:
https://doi.org/10.1090/qam/212364
MathSciNet review:
212364
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References |
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Additional Information
C. E. Billiglieimer, Solutions of a non-linear differential equation I, Proc. Camb. Phil. Soc. (1967–8)
F. Cap, Consequences of a nonlinear theory of nuclear forces, Nuovo Cimento Suppl, 807–812, (1956)
W. Heisenberg, Mesonenerzengung als Stosswell enproblem, Z. Phys. 133, 65–79, (1952)
- C. A. Hurst, An example of a divergent perturbation expansion in field theory, Proc. Cambridge Philos. Soc. 48 (1952), 625–639. MR 52333, DOI https://doi.org/10.1017/s0305004100076416
- D. F. Kurdgelaidze, Nonlinear scattering in electrodynamics and mesodynamics, Vestnik Moskov. Univ. 9 (1954), no. 8, 81–90 (Russian). MR 0071332
- A. Petermann, Renormalisation dans les séries divergentes, Helvetica Phys. Acta 26 (1953), 291–299 (French). MR 57181
L. I. Schiff, Nonlinear meson theory of nuclear forces, I: Neutral scalar meson with point-contact repulsion, Phys. Rev. 84, 1–9 (1951)
- J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
- Walter E. Thirring, Nichtlineare Terme in Meson-Gleichungen, Z. Naturforschung 7a (1952), 63–66 (German). MR 0050496
- Walter Thirring, On the divergence of perturbation theory for quantized fields, Helvetica Phys. Acta 26 (1953), 33–52. MR 53003
- Ryôyû Utiyama and Tsutomu Imamura, Difficulty of divergence of the perturbation method in the quantum field theory, Progr. Theoret. Phys. 9 (1953), 431–454. MR 56478, DOI https://doi.org/10.1143/ptp/9.4.431
C. E. Billiglieimer, Solutions of a non-linear differential equation I, Proc. Camb. Phil. Soc. (1967–8)
F. Cap, Consequences of a nonlinear theory of nuclear forces, Nuovo Cimento Suppl, 807–812, (1956)
W. Heisenberg, Mesonenerzengung als Stosswell enproblem, Z. Phys. 133, 65–79, (1952)
C. A. Hurst, An example of a divergent perturbation expansion in field theory, Proc. Cambridge Philos. Soc. 48, 625–639 (1952)
D. F. Kurdgelaidze, Nonlinear scattering in electrodynamics and mesondynamics, Vestn. Moskow Univ. 9, 8, 81–90, (1954)
A. Petermann, Renormalization dans les séries divergentes, Helv. Phys. Acta 26, 291–299 (1953)
L. I. Schiff, Nonlinear meson theory of nuclear forces, I: Neutral scalar meson with point-contact repulsion, Phys. Rev. 84, 1–9 (1951)
J. J. Stoker, Nonlinear vibrations, Interscience, New York, 1950
W. Thirring, Nichtlineare Terme in Meson-Gleichungen, Z. Natur-forsch. 7a, 63–66 (1952)
W. Thirring, On the divergence of perturbation theory for quantised fields, Helv. Phys. Acta. 26, 35–52 (1953)
R. Utiyama and T. Imamura, Difficulty of divergence of the perturbation method in quantum field theory, Progr. Theor. Phys. 9, 431–454 (1963)
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Article copyright:
© Copyright 1967
American Mathematical Society
