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arXiv · 2508.17534

A vectorial Darboux transformation for integrable matrix versions of the Fokas-Lenells equation

Folkert Müller-Hoissen·Rusuo Ye
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Abstract

Using bidifferential calculus, we derive a vectorial binary Darboux transformation for an integrable matrix version of the first negative flow of the Kaup-Newell hierarchy. A reduction from the latter system to an integrable matrix version of the Fokas-Lenells equation is then shown to inherit a corresponding vectorial Darboux transformation. Matrix soliton solutions are derived from the trivial seed solution. Furthermore, the Darboux transformation is exploited to determine in a systematic way exact solutions of the two-component vector Fokas-Lenells equation on a plane wave background. This comprises breathers, dark solitons, rogue waves and "beating solitons".

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Folkert Müller-Hoissen, Rusuo Ye. 2025-08-24. A vectorial Darboux transformation for integrable matrix versions of the Fokas-Lenells equation. https://arxiv.org/abs/2508.17534

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