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arXiv · 2501.04673

The Method of ${\cal M}_{n}$-Extension: The KdV Equation

Metin Gürses·Aslı Pekcan
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Abstract

In this work we generalize ${\cal M}_{2}$-extension that has been introduced recently. For illustration we use the KdV equation. We present five different ${\cal M}_{3}$-extensions of the KdV equation and their recursion operators. We give a compact form of ${\cal M}_{n}$-extension of the KdV equation and recursion operator of the coupled KdV system. The method of ${\cal M}_{n}$-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of ${\cal M}_{3}$-extension of KdV.

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Metin Gürses, Aslı Pekcan. 2025-01-08. The Method of ${\cal M}_{n}$-Extension: The KdV Equation. https://doi.org/10.1016/j.physleta.2024.130217

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