Linking reduced breaking crest speeds to unsteady nonlinear water wave
  group behavior

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Abstract

Observations show that maximally-steep breaking water wave crest speeds are much slower than expected. We report a wave-crest slowdown mechanism generic to unsteady propagating deep water wave groups. Our fully nonlinear computations show that just prior to reaching its maximum height, each wave crest slows down significantly and either breaks at this reduced speed, or accelerates forward unbroken. This finding is validated in our extensive laboratory and field observations. This behavior appears to be generic to unsteady dispersive wave groups in other natural systems.

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Is Open Access

Observation of Kuznetsov-Ma soliton dynamics in optical fibre

B. Kibler, J. Fatome, C. Finot … (2012)

The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.