On an integrable 2+1-dimensional extended Dym equation: Lax pair, $\bar{\partial}$-dressing scheme and modulation
Exactly Solvable and Integrable Systems
2026-03-11 v2 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.2601.05954,
title = {On an integrable 2+1-dimensional extended Dym equation: Lax pair, $\bar{\partial}$-dressing scheme and modulation},
author = {Boris Konopelchenko and Colin Rogers and Pablo Amster},
journal= {arXiv preprint arXiv:2601.05954},
year = {2026}
}