State Transition Induced by Self-Steepening and Self Phase-Modulation

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 phasemodulation (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.