Modulation instability and controllable rogue waves with multiple compression points for periodically modulated coupled Hirota equations

TL;DR

This paper derives rogue wave solutions for a variable-coefficients coupled Hirota equation, revealing controllable rogue waves with multiple compression points through modulation instability analysis and Darboux transformation.

Contribution

It introduces a hierarchy of rogue wave solutions with multiple compression points for the coupled Hirota equations, including explicit first and second-order solutions with novel wave structures.

Findings

Dark-bright and composite rogue waves with multiple compression points are demonstrated.

Generation of Peregrine combs from multiple compression points.

Wave characteristics like intensity difference and pulse energy are analyzed.

Abstract

Based on modulation instability analysis and generalized Darboux transformation, we derive a hierarchy of rogue wave solutions for a variable-coefficients coupled Hirota equations. The explicit first-order rogue wave solution is presented, and the dark-bright and composite rogue waves with multiple compression points are shown by choosing sufficiently large periodic modulation amplitudes in the coefficients of the coupled equations. Also, the dark-bright and composite Peregrine combs are generated from the multiple compression points. For the second-order case, the darkbright three sisters, rogue wave quartets and sextets structures with one or more rogue waves involving multiple compression points are put forward, respectively. Furthermore, some wave characteristics such as the difference between light intensity and continuous wave background, and pulse energy evolution of the dark rogue wave solution features multiple compression points are discussed.