Three-component coupled nonlinear Schrodinger system in a multimode optical fiber: Darboux transformation induced via a rank-two projection matrix

In this paper, the investigation is on a three-component coupled nonlinear Schr-Odinger (NLS) system which governs the wave evolution in a multimode optical fiber. We construct a Darboux transformation (DT) induced via a rank-two projection matrix, and then derive an (N, m)-generalized DT and the Nth-order solution, where the positive integers N and m denote the numbers of iterative times and distinct spectral parameters, respectively. Focusing on the Nth-order solution on the nonzero-zero-zero background, we derive two kinds of waves which could not be derived by the DT induced via a rank-one projection matrix, that is, the so-called fundamental nonlinear wave (N = 1) and degenerate fundamental nonlinear wave (N = 2 and m = 1). Via the asymptotic analysis, we find that the fundamental nonlinear wave is the nonlinear superposition of two dark-bright-bright solitons and a breather/Kuznetsov-Ma breather/rogue wave; and the degenerate fundamental nonlinear wave is the nonlinear superposition of four dark-bright-bright solitons and two breathers/two Kuznetsov-Ma breathers/a second-order rogue wave. Since such phenomena are not admitted for the one-component NLS equation and two-component coupled NLS system, they are more useful to understand the three-component coupled NLS system than what the latter two models admit. For other three-component coupled systems, more phenomena may be expected when the rank of projection matrix used to construct a DT is two rather than one, because our study presents an example. (C) 2021 Elsevier B.V. All rights reserved.