Moving boundary problems for a canonical member of the WKI inverse scattering scheme: conjugation of a reciprocal and Möbius transformation

Abstract

Abstract Reciprocal links between certain solitonic systems and their hierarchies are well-established. Moreover, the AKNS and WKI inverse scattering schemes are known to be connected by a composition of gauge and reciprocal transformations. Here, a reciprocal transformation allied with a Möbius-type mapping is applied to a class of Stefan-type problems for the solitonic Dym equation to generate a novel exact parametric solution to a class of moving boundary problems for a canonical member of the WKI system.