Coalescence and Droplets in the Subcritical Nonlinear Schrödinger Equation

We describe here the coalescence and formation of droplets, in a Hamiltonian kinetics of a first order phase transition. In the process of coalescence, the typical linear size of single phase domains grows as a power of time. The density correlation function follows the usual self-similar dynamic scaling. For different initial conditions, we observe the nucleation and dynamics of stable pulses. The stability of such pulses in one dimension is also computed. Both results may be relevant to superfluid He₄ cavitation or for filamentation in nonlinear optics and for the recent evidence of Bose-Einstein condensation in Li₇.