Super-regular breathers induced by the higher-order effects in coupled Hirota equations

We study the intriguing dynamics of surper-regular breathers (SRBs) beyond the Manakov system. These SRB solutions are derived within the nondegenerate context. By employing the Darboux transformation, we obtain the exact expressions of the solutions for the vector SRBs in the coupled Hirota equations with the third dispersion, self-steepening, and inelastic Raman scattering terms. Based on such explicit formulas, we initially study the higher-order effects on their group velocities as well as the growth rate during the linear stage of modulation instability (MI). Additionally, we conduct an exploration of various mode excitations emerging during the nonlinear stage of MI. Our findings indicate that there exist significantly different wave modes from those in the Manakov system or the scalar nonlinear Schr"odinger equation (NLSE). In particular, we refine existing formulas connecting the SRBs and MI in the nondegenerate regime, which eliminates the necessity to neglect higher-order terms from the Taylor expansion of $\ensuremath{\alpha}$. Instead, we have used four different eigenvalues for a more comprehensive description. We also discuss the scalar SRB with two eigenvalues using wave component analysis. We finally excite, via numerical simulation initiated with localized periodic initial conditions, the vector SRBs and their transformed states. This study not only deepens our theoretical comprehension of SRB dynamics, but also illuminates potential avenues for future experimental investigations in this fascinating field.