Generation of solitons by a boxlike pulse in the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

The creation of solitons of the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions from a boxlike initial pulse is considered. The inverse scattering transform is used. An equation for soliton eigenvalues is obtained. It is shown that simultaneous generation of breathers (solitons with internal oscillations) and one-parametric (nonoscillating) bright or dark solitons is possible. For some sets of initial parameters only breathers or only one-parametric solitons emerge. No more than three bright solitons can emerge (possibly, simultaneously with breathers) in any case, while dark solitons or breathers can arise in arbitrary number when the corresponding thresholds are exceeded. Analytical estimates for the number of generated solitons and the corresponding thresholds are given in some particular cases.