Solitons, numerical experiments, and that mysterious lady

Abstract

Dauxois replies: I did not attempt to present a complete history of the soliton concept, so all possibly relevant papers were not cited. However, I think the paper by Norman Zabusky and Martin Kruskal (J. E. Allen’s reference 1 1. T. Dauxois, M. Peyrard, Physics of Solitons, Cambridge U. Press, New York (2006).) ought to be emphasized for several reasons. First, it dealt directly with the understanding of the puzzling observation made by Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou. Second, it highlighted the soliton, a concept of general interest 1 1. T. Dauxois, M. Peyrard, Physics of Solitons, Cambridge U. Press, New York (2006). that goes beyond the observation of “collision free” wave interactions. Third, the suffix “-on” in the name emphasizes that those waves have properties of particles.I know that using a computer to solve an equation was done before FPU-Tsingou. (Working in physical oceanography and having a wife in fluid mechanics, I do respect meteorologists!) Solving equations, with or without approximations, is different from conducting a numerical experiment, which asks the computer a physical question. One studies a system simpler than the real one in order to use the computer to test theories that could not have been tested with real experiments, affected as they are by uncontrollable effects and noise (see the epistemological paper in reference 2 2. R. Livi, S. Ruffo, M. Pettini, A. Vulpiani, Giornale de Fisica 26(4), 285 (1985).). I am not aware of any previous use of computers in that way, nor, apparently, was Ulam. 3 3. S. M. Ulam, Adventures of a Mathematician, Scribner, New York (1976). REFERENCESSection:ChooseTop of pageREFERENCES <<1. T. Dauxois, M. Peyrard, Physics of Solitons, Cambridge U. Press, New York (2006). Google Scholar2. R. Livi, S. Ruffo, M. Pettini, A. Vulpiani, Giornale de Fisica 26(4), 285 (1985). Google Scholar3. S. M. Ulam, Adventures of a Mathematician, Scribner, New York (1976). Google ScholarScitation© 2008 American Institute of Physics.