Fermi-Pasta-Ulam Problem Research Articles

The Sine-Gordon Equation as a Model for a Rapidly Rotating Baroclinic Fluid

Recent work has shown that the Sine-Gordon and SIT equations describe the evolution of the envelope of baroclinic wave packets in a two-layer rapidly rotating fluid. The significance of this result is discussed with reference to the optical SIT problem and it is shown how this type of rotating fluid behaves in a simple way as a two-level pseudospin system. The periodic behaviour of the Sine-Gordon equation which is more appropriate for experimental situations is discussed. Experimental and numerical evidence suggests that recurrence of initial states occurs; behaviour which is strikingly similar to the FPU problem of solid state physics.

Fermi–Pasta–Ulam recurrence in the two-space dimensional nonlinear Schrödinger equation

Numerical solutions of the two-space dimensional nonlinear Schrödinger equation with spatially periodic boundary conditions have been obtained. It has been found that the long-time evolution exhibits the Fermi–Pasta–Ulam recurrence phenomenon for a wide range of initial conditions.

Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train

Results of an experimental investigation of the evolution of a nonlinear wave train on deep water are reported. The initial stage of evolution is found to be characterized by exponential growth of a modulational instability, as was first discovered by Benjamin ' Feir. At later stages of evolution it is found that the instability does not lead to wave-train disintegration or loss of coherence. Instead, the modulation periodically increases and decreases, and the wave train exhibits the Fermi–Pasta–Ulam recurrence phenomenon. Results of an earlier study of nonlinear wave packets by Yuen ' Lake, in which solutions of the nonlinear Schrödinger equation were shown to provide quantitatively correct descriptions of the properties of nonlinear wave packets, are applied to describe the experimentally observed wave-train phenomena. A comparison between the laboratory data and numerical solutions of the nonlinear Schrödinger equation for the long-time evolution of nonlinear wave trains is given.