  Numerical studies of dimple and jet formation from a collapsing cavity often
model the initial cavity shape as a truncated sphere, mimicking a bursting
bubble. In this study, we present a minimal model containing only nonlinear
inertial and capillary forces, which produces dimples and jets from a
collapsing, capillary wave trough. The trough develops from an initial
perturbation, chosen to be an eigen-mode to the linearised problem.We explain
the physical mechanism of dimple formation and demonstrate that, for moderate
steepness, the sharp dimple seen in simulations is well captured by the weakly
nonlinear theory developed here. For steepness >> 1 the regime is strongly
nonlinear spreading surface energy into many modes and the precursor dimple now
develops into a sharply rising jet. Here, simulations reveal a novel localised
window (in space and time) where the jet evolves self-similarly following
inviscid Keller & Miksis (1983) scales. We develop an analogy of this regime to
a self-similar solution of the first kind, for linearised, capillary waves. Our
first principles study demonstrates that at sufficiently small scales, dimples
and jets form due to radial focussing of capillary waves requiring (nonlinear)
inertial and capillary contributions, sans viscous or gravitational
interventions.
