A theory is developed for time-dependent coherent structures in a marginally stable atmospheric zonal flow. The coherent structures have the form of solitary waves travelling in the zonal direction. Analytical solutions are found for stationary solitary waves but these are shown to be always unstable. The instability manifests itself either as a fission of the structure subsequently emitting two oppositely directed travelling solitary waves or as an implosion in which the structure becomes increasingly more narrow and intense. Which of the two occurs depends sensitively on initial conditions. These solitary waves are stable in head-on collisions only if their joint zonally integrated amplitude is less than a critical value; otherwise, the implosion instability occurs. General initial conditions can give rise to solitary waves which either split, implode, or break down to form a train of nonlinear wave packets. A scenario for the birth and decay of isolated disturbances is given, utilizing the slow parametric transit of the marginal stability curve of the background zonal flow.