Zabusky, N. J.; Kruskal, M. D. Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states. (English) Zbl 1201.35174 Phys. Rev. Lett. 15, 240-243 (1965). From the text: We have observed unusual nonlinear interactions among “solitary-wave pulses” propagating in nonlinear dispersive media. These phenomena were observed in the numerical solutions of the Korteweg–de Vries equation \[ u_t+uu_x+\delta^2u_{xxx}=0. \tag{1} \] This equation can be used to describe the one-dimensional, long-time asymptotic behavior of small, but finite amplitude: shallow-water waves, collisionless plasma magnetohydrodynamic waves, and long waves in anharmonic crystals. Furthermore, the interaction and “focusing” in space-time of the solitary-wave pulses allows us to give a phenomenolocigal description of the near recurrence to the initial state in numerical calculations for a discretized weakly-nonlinear string made by Fermi, Pasta, and Ulam (FPU). Cited in 5 ReviewsCited in 613 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations 82D05 Statistical mechanics of gases 76X05 Ionized gas flow in electromagnetic fields; plasmic flow Keywords:unusual nonlinear interactions among solitary-wave pulses; nonlinear dispersive media; numerical solutions of Korteweg–de Vries equation PDF BibTeX XML Cite \textit{N. J. Zabusky} and \textit{M. D. Kruskal}, Phys. Rev. Lett. 15, 240--243 (1965; Zbl 1201.35174) Full Text: DOI OpenURL References: [1] J. J. Stoker, in: Water Waves (1957) [2] N. J. Zabusky, in: Proceedings of the Conference or Mathematical Models in the Physical Sciences (1963) [3] M. D. Kruskal, in: Progress on the Fermi, Pasta, Ulam Problem This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.