  A droplet bouncing on the surface of a vibrating liquid bath can move
horizontally guided by the wave it produces on impacting the bath. The wave
itself is modified by the environment, and thus the interactions of the moving
droplet with the surroundings are mediated through the wave. This forms an
example of a pilot-wave system. Taking the Oza Rosales Bush description for
walking droplets as a theoretical pilot-wave model, we investigate the dynamics
of two interacting identical, in-phase bouncing droplets theoretically and
numerically. A remarkably rich range of behaviors is encountered as a function
of the two system parameters, the ratio of inertia to drag, \k{appa}, and the
ratio of wave forcing to drag, \b{eta}. The droplets typically travel together
in a tightly bound pair, although they unbind when the wave forcing is large
and inertia is small or inertia is moderately large and wave forcing is
moderately small. Bound pairs can exhibit a range of trajectories depending on
parameter values, including straight lines, sub-diffusive random walks, and
closed loops. The droplets themselves may maintain their relative positions,
oscillate towards and away from one another, or interchange positions regularly
or chaotically as they travel. We explore these regimes and others and the
bifurcations between them through analytic and numerical linear stability
analyses and through fully nonlinear numerical simulation.

Fluid Dynamics;Chaotic Dynamics