Surfaces of Revolution via the Schroedinger Equation : Construction, Integrable Dynamics and Visualization

1997/10/30 by R. Beutler, Beutler, R., B. G. Konopelchenko +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematics and Applications #Relativity and Gravitational Theory #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9710027

29 pages, 27 figures

openalex publication_date 1997/10/30 · arxiv created 1997/11/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation (infinite well, harmonic oscillator, Coulomb potential, Bargmann potential, etc.) are analyzed and visualized. The properties of such surfaces are discussed. Two types of deformations (evolutions), namely 1) preserving the Gaussian curvature and 2) via the dynamics of the Korteweg-de-Vries equation are discussed.

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