Solitons, numerical experiments, and that mysterious lady

Abstract

The interesting article by Thierry Dauxois on “Fermi, Pasta, Ulam, and a Mysterious Lady” (Physics Today, Physics Today 0031-9228 61 1 2008 55 https://doi.org/10.1063/1.2835154. January 2008, page 55 ) relates the subject of solitons to that of the Fermi-Pasta-Ulam (FPU) problem. The term “soliton” was introduced by Norman Zabusky and Martin Kruskal 1 1. N. J. Zabusky, M. D. Kruskal, Phys. Rev. Lett. 15, 240 (1965). https://doi.org/10.1103/PhysRevLett.15.240 in 1965 because the nonlinear waves studied did not lose their identity after colliding. In a sense, they resembled particles. The study by Zabusky and Kruskal was a numerical one of the Korteweg–de Vries equation, but the motivation was to study the propagation of waves in a collisionless plasma containing a magnetic field. Fifty years ago John Adlam and I studied that problem 2 2. J. H. Adlam, J. E. Allen, Philos. Mag. 3, 448 (1958). https://doi.org/10.1080/14786435808236833 and found an analytical solution for strong, collision-free hydromagnetic solitary waves for Alfvén Mach numbers less than 2. The solution was not valid for faster, stronger waves. Further work in 1960 dealt with the excitation of a train of such waves; 3 3. J. H. Adlam, J. E. Allen, Proc. Phys. Soc. 75, 640 (1960). https://doi.org/10.1088/0370-1328/75/5/302 that time the equations were solved numerically. The work with Adlam seems to have been largely overlooked until recently, 4 4. F. Verheest, T. Cattaert, Phys. Plasmas 12, 032304 (2005). https://doi.org/10.1063/1.1853386 presumably because it predated the term “soliton.”REFERENCESSection:ChooseTop of pageREFERENCES <<1. N. J. Zabusky, M. D. Kruskal, Phys. Rev. Lett. 15, 240 (1965). https://doi.org/10.1103/PhysRevLett.15.240 , Google ScholarCrossref, ISI2. J. H. Adlam, J. E. Allen, Philos. Mag. 3, 448 (1958). https://doi.org/10.1080/14786435808236833 , Google ScholarCrossref3. J. H. Adlam, J. E. Allen, Proc. Phys. Soc. 75, 640 (1960). https://doi.org/10.1088/0370-1328/75/5/302 , Google ScholarCrossref4. F. Verheest, T. Cattaert, Phys. Plasmas 12, 032304 (2005). https://doi.org/10.1063/1.1853386 , Google ScholarCrossref, ISI© 2008 American Institute of Physics.