We give a fresh look at the famous problem investigated numerically by Zabusky and Kruskal in 1965 [1], i.e. the breaking of a harmonic wave in the weakly dispersing case and the associated Fermi-Pasta-Ulam recurrence. We report experimental results obtained for surface gravity waves in a shallow water tank [2]. We show that the results are accurately interpreted in terms of analytical formulas developed in the context of a WKB approach for the scattering problem associated with the the Korteweg-De Vries equation [3]. A parallel with experiments in optics described in terms of nonlinear Schrodinger equation is also proposed [4].

References

[1] N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett. 15, 240 (1965).

[2] S. Trillo, G. Deng, G. Biondini, M. Klein, G. F. Clauss, A. Chabchoub, M. Onorato, Hydrodynamical realisation and theoretical description of the Zabusky-Kruskal numerical experiment , submitted to Phys. Rev. Lett.

[3] G.. Deng, G. Biondini, and S. Trillo, Physica D, in press, doi:10.1016/j.physd.2016.03.003

[4] J. Fatome, C. Finot, G. Millot, A. Armaroli, and S. Trillo, Phys. Rev. X 4, 021022 (2014).