Novel equations demonstrate modulation effects in integrable systems, suggesting new insights in hydrodynamics.
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.
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Konopelchenko et al. (2026) studied this question.
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