  This paper presents a theoretical and experimental study of the long-standing
fluid mechanics problem involving the temporal resolution of a large, localised
initial disturbance into a sequence of solitary waves. This problem is of
fundamental importance in a range of applications including tsunami and
internal ocean wave modelling. This study is performed in the context of the
viscous fluid conduit system-the driven, cylindrical, free interface between
two miscible Stokes fluids with high viscosity contrast. Due to buoyancy
induced nonlinear self-steepening balanced by stress induced interfacial
dispersion, the disturbance evolves into a slowly modulated wavetrain and
further, into a sequence of solitary waves. An extension of Whitham modulation
theory, termed the solitary wave resolution method, is used to resolve the
fission of an initial disturbance into solitary waves. The developed theory
predicts the relationship between the initial disturbance's profile, the number
of emergent solitary waves, and their amplitude distribution, quantifying an
extension of the well-known soliton resolution conjecture from integrable
systems to non-integrable systems that often provide a more accurate modelling
of physical systems. The theoretical predictions for the fluid conduit system
are confirmed both numerically and experimentally. The number of observed
solitary waves is consistently within 1-2 waves of the prediction, and the
amplitude distribution shows remarkable agreement. Universal properties of
solitary wave fission in other fluid dynamics problems are identified.
