Abstract

The temporal resolution of a large localised initial disturbance into a sequence of solitary waves is the long-standing fluid mechanics problem. We propose an extension of Whitham modulation theory to describe the solitary wave fission process in a broad class of dispersive hydrodynamic systems.  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 processes. The main concrete example considered is the viscous fluid conduit system. The theoretical predictions of the method are confirmed both numerically and experimentally. This is joint work with Mark Hoefer’s Dispersive Hydrodynamics group at the University of Colorado Boulder.