State transition induced by self-steepening and self phase-modulation

TL;DR

This paper derives a rational solution to the MNLS equation demonstrating how self-steepening and self phase-modulation induce transitions among five distinct soliton states, including rogue waves, by tuning parameters.

Contribution

It introduces a new rational solution to the MNLS equation that reveals how self-steepening and SPM cause state transitions in soliton configurations.

Findings

Identifies five soliton states including rogue waves.

Shows state transitions are controlled by parameters a and b.

Highlights the fundamental role of self-steepening and SPM in soliton dynamics.

Abstract

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.