R. Beutler et Bg. Konopelchenko, Surfaces of revolution via the Schrodinger equation: Construction, integrable dynamics and visualization, APPL MATH C, 101(1), 1999, pp. 13-43
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 Schrodinger equation (infinite well, harmonic oscilla
tor, Coulomb potential, Bargmann potential, etc.) are analyzed and visualiz
ed. The properties of such surfaces are discussed. Two types of deformation
s (evolutions) of the surfaces of revolution, namely (1) preserving the Gau
ssian curvature and (2) via the dynamics of the Korteweg-de Vries (KdV) equ
ation are discussed. (C) 1999 Elsevier Science Inc. All rights reserved.