Rogue waves for a system of coupled derivative nonlinear Schr\"odinger equations

TL;DR

This paper explores rogue waves in coupled derivative nonlinear Schrödinger equations, revealing new regimes of modulation instability and rogue wave formation influenced by group velocity mismatch and self-steepening effects.

Contribution

It demonstrates for the first time that coupled DNLSEs can produce rogue waves under conditions different from standard NLSEs, considering self-steepening and velocity mismatch.

Findings

Rogue waves depend on group velocity mismatch and nonlinear parameters.

New regimes of modulation instability identified for coupled DNLSEs.

Rogue waves exhibit different amplification ratios and existence criteria.

Abstract

Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schr\"odinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics and plasmas, exhibits RWs only in the regime of modulation instability (MI) of the background. For system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect will be demonstrated for a system of coupled derivative NLSEs (DNLSEs), where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs will depend on the mismatch in group velocities between the components, as well as the parameters for cubic nonlinearity and self-steepening. RWs considered in this work differ from those of the NLSEs in terms of the amplification ratio and criteria of existence. Applications to optics and plasma physics are discussed.