Solitons and radiation described by the derivative nonlinear Schroedinger equation

We analyze the limits of validity of a previously found distribution function of solitons [S. Ponce Dawson and C. Ferro Fontan, Phys. Rev. A 39, 5289 (1989)] when applied to the derivative nonlinear Schroedinger equation. This function allows an easy determination of the solitons that evolve from a given initial condition. We are particularly interested in weakly unstable cases that generate anomalous solitons. We study this case both analytically and numerically. We conclude that the distribution function describes a subset of the solitons correctly. An additional term obtained by Mjolhus (private communication) must be added to take into account the most energetic anomalous solitons. The complete distribution fits the simulations quite accurately, even in situations that do not satisfy the necessary conditions discussed by Dawson and Fontan