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arXiv · 2601.05954

On an integrable 2+1-dimensional extended Dym equation: Lax pair, $\bar{\partial}$-dressing scheme and modulation

Boris Konopelchenko·Colin Rogers·Pablo Amster
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Abstract

In 1+1-dimensions, an extension of the canonical solitonic Dym equation has previously been derived both in a geometric torsion evolution context and in the analysis of peakon solitonic phenomena in hydrodynamics. Here, a novel 2+1-dimensional S-integrable extended Dym-type equation is introduced. As Lax pair is constructed and an associated $\bar{\partial}$-dressing scheme detailed. Integrable modulated versions of the 2+1-dimensional extended Dym equation are generated via application of a class of involutory transformations with genesis in classical Ermakov theory.

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Boris Konopelchenko, Colin Rogers, Pablo Amster. 2026-01-09. On an integrable 2+1-dimensional extended Dym equation: Lax pair, $\bar{\partial}$-dressing scheme and modulation. https://doi.org/10.46298/ocnmp.17315

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