You had me at "sheep soliton".
Yes, under a suitable approximation, it appears that you can gave a
soliton description of certain types of collective behavior in sheep.
Below are the title and abstract. (I was hoping for an intriguing picture from the experimental data, but alas the visuals in this article are run-of-the-mill.) In other contexts, when sheep (a type of
'active matter') behave
like a fluid, there are obvious jokes to tell about "shearing instabilities".
Title: Sheep Soliton
Abstract: Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioral rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronizing when they decide to switch between the two modes. We propose a model for the individual decision making process and parametrize it from data. Next, we translate this individual-based model into its density-flow equations counterpart, considering 1D-motion along the group trajectory. Numerical solving these equations display a solitary wave propagating at constant speed. Coupling individual and collective levels, groups motion can then be seen as a wave propagating at some fraction of the individual walking speed even though each individual is at any moment either stopped or walking. Considering the minimal model embedded in these equations, we show analytically that it has the Korteweg-De Vries (KdV) Soliton as a steady regime solution. This soliton emerges from the non linear coupling of start/stop individual decisions which compensate exactly for diffusion and promotes a steady ratio of walking / stopped individuals, which in turn determines the wave speed. The convergence to only one solitary wave from any initial condition, and which can recover from perturbation, gives a high robustness to this biological system.
Update (12/18/17): I forgot to make a snarky remark along the following lines: One first needs to do a continuum approximation to get a relevant nonlinear wave equation.
For the actual sheep, one would think that there is some energy shedding as the wave propagates. :)
