Generalized Darboux transformation and higher-order rogue wave solutions to the Manakov system - Mukam, Serge P.; Abbagari, Souleymanou; Houwe, Alphonse; Kuetche, Victor K.; İnç, Mustafa; Doka, Serge Y.; Akinlar, Mehmet Ali (World Scientific Publ Co Pte Ltd, 2021)
In this paper, we propose a recursive Darboux transformation in a generalized form of a focusing vector Nonlinear Schrodinger Equation (NLSE) known as the Manakov System. We apply this generalized recursive Darboux transformation to the Lax-pairs of this system in view of generating the Nth-order vector generalization rogue wave solutions with a rule of iteration. We discuss from first- to three-order vector generalizations of rogue wave solutions while illustrating these features with some 3D, 2D graphical depictions. We illustrate a clear connection between higher-order rogue wave solutions and their free parameters for better understanding the physical phenomena described by the Manakov system
Keywords: Darboux transformation; NLSE; higher-order rogue waves; Manakov system