A Theory of Matter and Electricity by Birkhoff G.D.

By Birkhoff G.D.

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19, 1095-1097 (1967). 24. 25. , Commun. Pure Appl. Math. 21, 467-490 (1968). , J. Phys. Soc. Japan, 22, 431-436 (1967). See also ibid. 23, 501-506 (1967); 26 235-237 (1969); and 34, 18-25 26. , J. Fluid Mech. 22, 273-283 (1965); ibid. 27, Roy. 399-412 (1967); ibid. 44, 373-395 (1970). Also Proc. Soc. A 283, 238-261 (1965) and 299, 6-25 (1967). This work is conveniently summarized in Whitham's recent book: Linear 27. C. ) Nonlinear (1973); Phys. Reports and Waves, Appl. 28. 29. 30. 31. 32. 33. Nonlinear Math.

Nor would it have been a surprise to Seeger, Donth and Kochendorfer 50 Alwyn C. Scott who had noted in 1953 the connection between this early work and the paper by Frenkel and Kontorova [16]. But Perring and Skyrme were interested in (12) as a one-dimensional model for an elemen­ tary particle, and, in this context, one supposes that the com­ plete absence of scattering might have been a bit disappointing. Throughout the 1960's (12) arose in a wide variety of problems in applied science (including the propagation of ferromagnetic domain walls, the "self-induced transparency" effect in nonlinear optics, and propagation of magnetic flux quanta on Josephson transmission lines) and eventually became known as the "sineGordon" equation [22].

35. 36. 37. , "Asymptotic Behavior of the Solutions of Systems of Differential Equations with a Small Parameter in the Higher Derivatives," Trans. RMS (2) 18, 295-319 (1961). , "Asymptotic Calculation of Periodic Solu­ tions of Systems of Differential Equations Containing Small Parameters in the Derivatives," Trans. AMS (2) 18, 199-230 (1961). , "Differential Equations, Stability, Oscilla­ tions, Time Lags," Academic Press, New York (1966). , "Perturbation Methods," Wiley, New York (1973). , Pasta, J.

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