On an integrable 2+1-dimensional extended Dym equation: Lax pair, ∂-dressing scheme and modulation

2026/01/09 by Boris Konopelchenko, Colin Rogers, Pablo Amster · 1 voice
Physics and Astronomy · Mathematics · #nlin.SI #math.CA

paper · pdf · doi:10.46298/ocnmp.17315

arxiv published 2026/01/09 · arxiv updated 2026/02/02

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 ∂-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.

Citations

• Solutions to the Kaup--Broer System and Its 2+1 Dimensional Integrable Generalization via the Dressing Method
• Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System
• A Novel Ermakov–Painlevé II System: ‐Dimensional Coupled NLS and Elastodynamic Reductions
• On a 2+1‐Dimensional Whitham–Broer–Kaup System: A Resonant NLS Connection
• An integrable shallow water equation with peaked solitons

Discussions

• Boris Konopelchenko, Colin Rogers, Pablo Amster: On an integrable 2+1-dimensional extended Dym equation: Lax pair, $\bar{\partial}$-dressing scheme and modulation https://arxiv.org/abs/2601.05954 http [bsky, 0 points, 0 comments]

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