https://doi.org/10.1140/epjs/s11734-025-01858-8
Regular Article
Mixed semirational solutions in the three-component Lakshmanan–Porsezian–Daniel equation
School of Mathematics and Information Science, Zhengzhou University of Light Industry, 450002, Zhengzhou, Henan, China
Received:
8
May
2025
Accepted:
8
August
2025
Published online:
19
August
2025
The three-component Lakshmanan–Porsezian–Daniel equation, which always describe the ultrashort pulses in the birefringent optical fiber, is investigated by the Darboux transformation (DT) method. Based on the Lax pair, the N-fold DT formulae are successfully derived in compact determinant representations. Employing the limiting technique in the proposed DT, we will mainly derive three different kinds of semirational solutions: (1) higher order RWs coexisting with multi-bright solitons, (2) higher order RWs interacting with multi-dark solitons, and (3) higher order RWs interplaying with multi-breather solutions. Considering different combinations of the above received three kinds of solutions in these three components 
, 
and 
, we successfully generate four mixed semirational solutions. To our knowledge, the above-mentioned four mixed semirational solutions cannot be derived in neither the single- or two-component nonlinear systems. In view of these results, the multi-component nonlinear systems are further suggested to own more novel and interesting dynamics than uncoupled ones.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
