  We present a rational solution for a mixed nonlinear Schr\"odinger (MNLS)
equation. This solution has two free parameters $a$ and $b$ representing the
contributions of self-steepening and self phase-modulation (SPM) of an
associated physical system. It describes five soliton states: a paired
bright-bright soliton, single soliton, a paired bright-grey soliton, a paired
bright-black soliton, and a rogue wave state. We show that the transition among
these five states is induced by self-steepening and SPM through tuning the
values of $a$ and $b$. This is a unique and potentially fundamentally important
phenomenon in a physical system described by the MNLS equation.
