Exact solutions for the coagulation-fragmentation equation

The authors present new exact equilibrium and time-dependent solutions to the two main versions of the coagulation-fragmentation equation. Equilibria are first found for the pure coagulation and pure fragmentation equations; equilibrium solutions for the full coagulation-fragmentation equation are then constructed when the kernels governing the reaction rates are chosen to be in a particular form. Time-dependent solutions are also derived for the pure fragmentation equation.