Abstract
A class of moving boundary problems for the solitonic potential mkdV equation is set down which is reciprocal to generalised Stefan-type problems that admit exact solution in terms of a Painleve II symmetry reduction. The latter allows the construction of the exact solution of the moving boundary problems via the iterated action of a Backlund transformation. This results in solution representation in terms of Yablonski–Vorob’ev polynomials. It is indicated how the results may be extended, via a novel reciprocal link, to moving boundary problems for a canonical solitonic equation generated as a member of the WKI inverse scattering system.
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