Rogue wave pattern of multi-component derivative nonlinear Schrodinger equations

Abstract: This paper delves into the study of multi-component derivative nonlinear Schrodinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation (DT) method, we derive higher-order vector rogue wave solutions for the n-DNLS equations. Specifically, we focus on the distinctive scenario where the (n + 1)-order characteristic polynomial possesses an explicit (n + 1)-multiple root. Additionally, we provide an in-depth analysis of the asymptotic behavior and pattern classification inherent to the higher-order vector rogue wave solution of the n-DNLS equation, particularly when one of the internal parameters attains a significant magnitude. These patterns are related to the root structures in the generalized Wronskian-Hermite polynomial hierarchies.