Solutions to the Calapso Equation Associated with Surfaces of Revolution
DOI:
https://doi.org/10.17268/sel.mat.2026.01.02Keywords:
Calapso equation, Zoomeron and Davey–Stewartson III equations, Ribaucour transformations, isothermic surfacesAbstract
We construct explicit solutions of the Calapso equation by applying Ribaucour transformations to isothermic surfaces of revolution. We derive conditions under which such transformations preserve the isothermic structure and generate new solutions of the Calapso equation. The resulting solutions depend on three functions, two depending on one variable and one depending on another variable. As a consequence, we obtain solutions of the Zoomeron and Davey–Stewartson III equations. Explicit examples associated with the cylinder, cone and catenoid are provided.
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