Higher-order soliton, rogue wave and breather solutions of a generalized Fokas–Lenells equation

Jiao Wei, Jiajia Li, Minxin Jia and Xin Wang

Chaos, Solitons & Fractals, 2025, vol. 195, issue C

Abstract: Under investigation is a generalized Fokas–Lenells equation, which is the first nontrivial equation in the negative hierarchy flow associated with a 2 × 2 matrix spectral problem involving two potentials. Based on the N-fold classical Darboux transformation, the (n, N-n)-fold generalized Darboux transformation is constructed by means of the limit technique. As an application, the higher-order localized wave solution in a compact determinant form with arbitrary order is derived for the generalized Fokas–Lenells equation. The bright-dark soliton solutions from first to third order under a zero background are obtained. Specifically, unlike the bright rogue wave and breather solutions of the standard Fokas–Lenells equation, the bright-dark and bright-bright rogue wave solutions as well as breather solutions from first to third order under a nonzero background of the generalized Fokas–Lenells equation are presented. Furthermore, the hybrid rogue wave-breather solutions from second to third order are given. The dynamical behaviors of these explicit solutions are all displayed graphically.

Keywords: Fokas–Lenells equation; Soliton; Rogue wave; Breather; Generalized Darboux transformation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:195:y:2025:i:c:s0960077925002656

DOI: 10.1016/j.chaos.2025.116252

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