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On a class of moving boundary problems for the potential mkdV equation: conjugation of Bäcklund and reciprocal transformations

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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 Painlevé II symmetry reduction. The latter allows the construction of the exact solution of the moving boundary problems via the iterated action of a Bäcklund 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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  1. Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems, School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW, 2052, Australia

    Colin Rogers

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  1. Colin Rogers
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Rogers, C. On a class of moving boundary problems for the potential mkdV equation: conjugation of Bäcklund and reciprocal transformations. Ricerche mat 65, 563–577 (2016). https://doi.org/10.1007/s11587-016-0275-y

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  • DOI: https://doi.org/10.1007/s11587-016-0275-y

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