On the multi-component Fokas–Lenells system: KP reductions and various soliton solutions

Abstract

In this paper, the multi-component Fokas–Lenells (mFL) system is studied by Hirota’s bilinear method and Kadomtsev–Petviashvili (KP)-Toda reduction approach. We demonstrate that the bilinear equations of the mFL system and their Gram-type determinant solutions can be reduced from a set of bilinear equations in the KP-Toda hierarchy. Moreover, we derive the set of bilinear equations from the discrete KP hierarchy by Miwa transformation. Dark solitons, breathers, and resonant breathers are presented. In particular, the breathers are classified into three different types, such as Akhmediev breather and Kuznetsov–Ma breather. The resonance phenomena of the breathers are also investigated. We give three- and four-resonant breather solutions for the three-component Fokas–Lenells system. Dynamics of the derived solutions are illustrated and analyzed.