Miura transformation in bidifferential calculus and a vectorial Darboux transformation for the Fokas–Lenells equation
Folkert Müller-Hoissen, Rusuo Ye
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Source: Crossref
Published: Jul 15, 2025
DOI: 10.1088/1751-8121/adebc6
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Abstract Using a general result of bidifferential calculus and recent results of other authors, a vectorial binary Darboux transformation is derived for the first member of the ‘negative’ part of the potential Kaup-Newell hierarchy, which is a system of two coupled Fokas–Lenells equations. Miura transformations are found from the latter to the first member of the ‘negative’ part of the AKNS hierarchy and also to its ‘pseudodual’. The reduction to the Fokas–Lenells equation is implemented and exact solutions with a plane wave seed generated.
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