3 papers
math.CA2025
Confluent Darboux transformations and Wronskians for algebraic solutions of the Painlevé III () equation
J. W. E. Harrow, A. N. W. Hone
We describe the use of confluent Darboux transformations for Schrödinger operators, and how they give rise to explicit Wronskian formulae for certain algebraic solutions of Painlev…
math-ph2025
Special solutions of a discrete Painlevé equation for quantum minimal surfaces
Peter A. Clarkson, Anton Dzhamay, Andrew N. W. Hone +1
We consider solutions of a discrete Painlevé equation arising from a construction of quantum minimal surfaces by Arnlind, Hoppe and Kontsevich, and in earlier work of Cornalba and…
nlin.SI2024
Casting more light in the shadows: dual Somos-5 sequences
J. W. E. Harrow, A. N. W. Hone
Motivated by the search for an appropriate notion of a cluster superalgebra, incorporating Grassmann variables, Ovsienko and Tabachnikov considered the extension of various recurre…