Multi-component Nonlinear Schrödinger Equations with Nonzero Boundary Conditions: Higher-Order Vector Peregrine Solitons and Asymptotic Estimates

We first report the first- and higher-order vector Peregrine solitons (alias rational rogue waves) for any multi-component NLS equations based on loop group theory, an explicit (n + 1)-multiple eigenvalue of a characteristic polynomial degree 1) related to condition Benjamin-Feir instability, inverse functions. Particularly, these waves are parity-time symmetric some parameter constraints. A systematic effective approach is proposed study asymptotic behaviors such that decompositions so-called governing polynomials, which pave powerful way in wave structures integrable systems. The with maximal amplitudes can be determined via vectors, interesting useful physical