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Moving boundary problems for the Harry Dym equation and its reciprocal associates

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Abstract

Moving boundary problems of generalised Stefan type are considered for the Harry Dym equation via a Painlevé II symmetry reduction. Exact solutions of such nonlinear boundary value problems are obtained in terms of Yablonski–Vorob’ev polynomials corresponding to an infinite sequence of values of the Painlevé II parameter. The action of two kinds of reciprocal transformation on the moving boundary problems is described.

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  1. Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems, School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Colin Rogers

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Rogers, C. Moving boundary problems for the Harry Dym equation and its reciprocal associates. Z. Angew. Math. Phys. 66, 3205–3220 (2015). https://doi.org/10.1007/s00033-015-0567-1

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