Journal of Experimental and Theoretical Physics

, Volume 114, Issue 2, pp 343–353 | Cite as

The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin

  • V. P. Ruban
Statistical, Nonlinear, and Soft Matter Physics


Different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear “one-dimensional” potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in analytic form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on the number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is the appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either the appearance of tall waves or the formation of sharp crests at moderate-height waves.


Soliton Rogue Wave Extreme Wave Shallow Water Wave Soft Matter Phys 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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